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FermilabRecycler Ring

TechnicalDesign Report

November 1996

Revision 1.2

Table of Contents

1. Introduction1.1. Role in the Fermilab III Program1.2. Performance1.3. Operational Roles1.4. Organization of this Report

2. Accelerator Physics2.1. Operational Overview2.2. Lattice Issues2.3. Performance Projections and Modeling2.4. Beamlines and Beam Transfers2.5. Vacuum Issues2.6. RF System2.7. Impedances and Instabilities2.8. Intrabeam Scattering2.9. Stochastic Cooling

3. Technical Components3.1 Magnets (WBS 3.1.1.)3.2 Vacuum (WBS 3.1.2.)3.3 Power Supplies (WBS 3.1.3.)3.4 RF Systems (WBS 3.1.4.)3.6 Kickers (WBS 3.1.6.)3.7 Stochastic Cooling (WBS 3.1.7.)3.8 Instrumentation (WBS 3.1.8.)3.9 Controls (WBS 3.1.9.)3.10 Safety System (WBS 3.1.10.)3.11 Utilities (WBS 3.1.11.)

4. Civil Construction4.1. Stochastic Cooling Penetrations4.2. Stochastic Cooling Telescope

5. Appendices5.1. Lattice5.2. Cost Estimate5.3. Schedule

November 5, 1996 1.3 Fermilab Recycler RingRevision 1.2 Technical Design Report

1. Introduction

This report describes the technical design of the Fermilab Recycler Ring. Thepurpose of the Recycler is to augment the luminosity increase anticipated from theimplementation of the Fermi III upgrade project, which has as its main component theFermilab Main Injector construction project.

The Recycler is a fixed 8 GeV kinetic energy storage ring. It is located in the MainInjector tunnel directly above the Main Injector beamline, near the ceiling. Theconstruction schedule calls for the installation of the Recycler ring during the installationof the Main Injector. This aggressive construction schedule is made possible by theexclusive use of permanent magnets in the ring lattice, removing the need for expensiveconventional iron/copper magnet construction along with the related power supplies,cooling water system, and electrical safety systems. The location, operating energy, andmode of construction are chosen to minimize operational impacts on both Fermilab'songoing High Energy Physics program and the Main Injector construction project.

1.1 Role in the Fermilab III Program

The Tevatron Collider provides the highest energy collisions in the world. To fullyexploit this unique tool, Fermilab is committed to a program of accelerator upgrades forthe purpose of increasing the Collider luminosity. Over the past 7 years the luminosityhas been increased from a typical peak of 1.6x1030 cm-2sec-1 in 1989 to over 2x1031 cm-

2sec-1 during 1995. Note that the original design peak luminosity of the TevatronCollider was 1.0x1030 cm-2sec-1.

The Main Injector will supply a larger flux of protons for antiproton production, moreintense proton bunches for use in the Collider, and a higher efficiency acceleration ofantiprotons. The role of the Recycler ring is to provide more antiprotons for theTevatron, which proportionally increases the luminosity. This is accomplished by actingas a high reliability post-Accumulator and receptacle for recycled antiprotons from theprevious Collider store. Prior to the development of the Recycler ring, the peakluminosity goal of the Fermi III upgrade program was 8x1031 cm-2 sec-1. With theconstruction of the Recycler ring, a typical peak luminosity of 2x1032 cm-2 sec-1 isexpected. This factor of 2-3 increase in luminosity comes from the availability of moreantiprotons at Tevatron injection. The Reycler is also the foundation of future acceleratorupgrades which can generate another order of magnitude luminosity increase up to anultimate goal of greater than 1x1033 cm-2sec-1. This report documents the design of thenew fixed-energy Recycler storage ring to be placed in the Main Injector tunnel.

Figure 1.1 displays the history of the typical peak luminosity as a function of timesince 1989, which shows an exponential growth with a doubling time of 1.5 years. Withthe addition of the Recycler ring and its commissioning along with the Main Injector, theTevatron Collider will be able to remain on this exponential slope. The first open pointrepresents the initial typical peak luminosity goal of the Main Injector project. Thesecond open point represents the luminosity goal of 2x1032 cm-2sec-1 during ColliderRun II when the Recycler is added to the picture. It should be possible, with further


accelerator upgrades, to achieve a luminosity of 1x1033 cm-2sec-1, which is the highestluminosity open point in figure 1.1.

1

10

100

1000

1988 1990 1992 1994 1996 1998 2000 2002 2004

Year

Tev

atro

n C

ollid

er L

umin

osity

(10

30 c

m-2

sec-1

)

Design Luminosity

Doubling Time = 1.5 Years

Figure 1.1: Tevatron Collider luminosity as a function of time. The filledcircles are measured "best typical" peak luminosities, the line is anexponential fit to the data, and the open points represent goals for thefuture.

1.2. Performance

The Recycler ring parameter list is given in table 1.1. The placement and design ofthe ring were chosen to minimize its impact on the existing high energy physics program.This minimization takes place mostly in the areas of project cost and schedule. After theend of the present fixed target run, the only scheduled prolonged accelerator shutdownbefore the start of LHC operations at CERN is the 1998 Main Injector connection to theTevatron. In the interest of accumulating the maximum amount of integrated luminositybefore the LHC is publishing high energy physics results, an additional Tevatronshutdown for installation of the Recycler would be highly undesirable. By using as manyof the already established Main Injector subsystem and lattice designs as possible, theability to finish the Recycler installation before the completion of the Main Injector ismade possible.


Table 1.1: Recycler ring parameter list.

Circumference 3319.400 mMomentum 8.889 GeV/cNumber of Antiprotons 2.5x1012

Maximum Beta Function 55 mMaximum Dispersion Function 2.0 mHorizontal Phase Advance per Cell 86.8 degreesVertical Phase Advance per Cell 79.3 degreesNominal Horizontal Tune 25.425Nominal Vertical Tune 24.415Nominal Horizontal Chromaticity -2Nominal Vertical Chromaticity -2Transition Gamma 20.7

Transverse Admittance 40 π mmmrFractional Momentum Aperture 1%

Superperiodicity 2Number of Straight Sections 8Number of Standard Cells in Straight Sections 18Number of Standard Cells in Arcs 54Number of Dispersion Suppression Cells 32Length of Standard Cells 34.576 mLength of Dispersion Suppression Cells 25.933 m

Number of Gradient Magnets 108/108/128Magnetic Length of Gradient Magnets 4.267/4.267/2.845 mBend Field of Gradient Magnets 1.45/1.45/1.45 kGQuadrupole Field of Gradient Magnets 3.6/-3.6/7.1 kG/mSextupole Field of Gradient Magnets 3.3/-5.9/0 kG/m2

Number of Lattice Quadrupoles 72Magnetic Length of Quadrupoles 0.5 mStrength of Quadrupoles 30 kG/m

The other, more important, means of insuring prompt construction of the Recyclerring is to keep the cost very low. In order to achieve this feat, all subsystems must bedesigned to be simultaneously lower cost. For instance, the biggest cost savings comesfrom placing the Recycler ring in the Main Injector tunnel and avoiding civilconstruction. Taking advantage of the fact that this ring operates at a fixed momentum,the magnets are built using permanent strontium ferrite magnets. By designing the


magnets to require very little human labor in their construction, a substantial costreduction is realized. Minimizing the number of magnets is accomplished by merging thequadrupole and dipole functions into gradient magnets. Because the magnetic field ispermanent, no power supplies, LCW cooling systems, power distribution cables, orelectrical safety systems are required. Since the permanent magnets are very stableagainst time and temperature, distributed correction magnets are also not needed.

In addition, technological advancements in beam pipe preparation have led tosuperior vacuum pressures at lower cost. Stochastic cooling is employed to provide thephase space density necessary for Tevatron Collider operations. By recycling many ofthe components used in the Tevatron bunched beam stochastic cooling R&D project, andminimizing the design costs for the pickup and kicker tanks by copying old Accumulatortanks, the cost of this subsystem is also minimized. The cost of instrumentation is alsoreduced through technological innovation, but these saving are reinvested back into thering to provide more detailed and precise measurements of beam parameters.

The design kinetic energy of the Recycler ring is precisely 8.000 GeV. This is thedesign kinetic energy of the Accumulator, as well as the injection kinetic energy of theMain Injector and extraction kinetic energy of the Booster. In the past considerabledebate has occurred regarding the measurement and synchronization of this energybetween these accelerators. With the planned construction of the Recycler with fixedfield permanent magnets, an unambiguous energy reference is installed into the Fermilabaccelerator complex. All other accelerators will be energy matched to the Recycler.

1.3. Operational Roles

The purpose of the Recycler is to further increase the luminosity of the TevatronCollider over the luminosity goals of the Main Injector by itself. The majority of theluminosity improvement comes from the ability to inject more antiprotons into theTevatron each store.

The first role of the Recycler is to act as a high reliability storage ring for antiprotons.Because there are few power sensitive components, there are virtually no mechanisms forinadvertent beam loss. Studying the data from the existing Antiproton Source complex,composed of the Debuncher and Accumulator rings, a couple of recent statistics ratifythis concern.

In 35 weeks of running, the total number of antiprotons stacked was 16.72x1013. Inthe same time interval, the total number of antiprotons lost or dumped was 2.42x1013,which is 14.5% of antiprotons stacked. Additionally, there were 506 hours of AntiprotonSource downtime out of a total of 9552 hours of operation (5.3% downtime). It is notimpossible to lose the beam in the Recycler, so some of the types of failures found in theAccumulator will also occur in the Recycler. Therefore, the percentage improvement inantiproton availability with the use of the Recycler will not be the full 14.5%.

The second role of the Recycler is to act like a post-Accumulator ring. As the stacksize in the Accumulator ring increases, there comes a point when the stacking rate startsto decrease. By emptying the contents of the Accumulator into the Recycler periodically,the Accumulator is always operating in its optimum antiproton intensity regime.


The third role of the Recycler, and by far the leading factor in luminosity increase, isto act as a receptacle for antiprotons left over at the end of Tevatron stores. By coolingthese antiprotons and reintegrating them into the Recycler stack, the effective stackingrate, and hence the luminosity, is more than doubled.

1.4. Organization of this Report

This report is organized into four chapters. Chapter 1 is the introduction. Chapter 2is the summary of the accelerator physics issues of the Recycler ring and beamlines.Chapter 3 contains a description of the technical component subsystems as well asoverviews of design specifications. Discussions and descriptions of technical componentsubsystems are organized to follow the Work Breakdown Structure (WBS) of the project.All technical components are contained in WBS category 3.1. The third digit of the WBSdescribes the component type: 1=magnets, 2=vacuum, 3=power supplies, etc. Chapter 4summarizes the civil construction for the Recycler.

November 5, 1996 2.1 Fermilab Recycler RingRelease 1.2 Technical Design Report

2. Accelerator Physics

The purpose of the Recycler ring is to improve the luminosity performance of theTevatron Collider during Run II. The design luminosity of 2x1032 cm-2 sec-1 isaccomplished by creating more antiprotons at a faster rate, storing existing antiprotons ina more reliable fashion, and recycling antiprotons remaining in the Tevatron at the end ofstores. The Recycler ring plays a major role in each of these three areas of improvement.

In this chapter the role of accelerator physics and novel technologies in the Recyclerare reviewed. This discussion starts with a detailed overview of the operational role ofthe Recycler during Run II. Next, the beam manipulations and accelerator technologycrucial to the Recycler are described.

2.1. Operational Overview

In order to describe the operational role of the Recycler ring, it is necessary to explainthe intricately interweaved operation of all of the particle accelerators in the entireaccelerator complex. It is convenient to start this discussion when the Tevatron has juststarted a new store.

2.1.1. Operational Goals

The purpose of the Fermi III accelerator upgrades is to maximize the luminosity ofthe Tevatron Collider. In the absence of a crossing angle the luminosity per interactionregion L is determined by the equation

L =Np NaB( )fo 6βrγ r( )

2π β* εnp + εna( ) Hβ*

12 σsp

2 + σsa2( )

, (2.1.1)

in which Np,a is the number of protons and antiprotons per bunch, B is the number ofbunches per beam, fo is the revolution frequency of the Tevatron, βr and γr are therelativistic velocity and energy of the beam, β* is the value of the beta function at theinteraction points, εnp,na are the proton and antiproton 95% normalized transverseemittances, σs is the rms bunch length, and the hour-glass luminosity form factor has theform

H x( ) = π x 1 − Φ(x)[ ] ex2, (2.1.2)

where Φ(x) is the error function. The transverse emittance is defined so that thetransverse rms bunch widths are calculated using the equation

σa,p2 = β* εna,np

6βrγ r( ) . (2.1.3)


The values for all of these parameters at the beginning of a store for Run I operations,anticipated after completion of the original Main Injector project, and aftercommissioning of the Recycler ring are listed in table 2.1.1.

Table 2.1.1: Initial Beam conditions for Run I (recently completed),originally anticipated post-Main Injector Run II, and Run II in which theRecycler ring is operational.

Initial Store Parameters Run I MI only Recycler

Np Proton Intensity/Bunch (109) 250 330 270Na Antiproton Intensity/Bunch (109) 60 36 66B Number of Bunches/Beam 6 36 36 Minimum Time between Bunches (ns) 3500 395 395 (132)

Eo Beam Energy (GeV) 900 1000 1000

β* Interaction Point Beta (cm) 35 35 35εnp Proton 95% Emittance (π mmmr) 24 30 18εna Antiproton 95% Emittance (π mmmr) 15 15 15σsp Rms Proton Bunch Length (cm) 50 45 45σsa Rms Antiproton Bunch Length (cm) 50 45 33fo Revolution Frequency (kHz) 47.7 47.7 47.7

(NaB) Total Antiproton Intensity (1010) 36 130 238(βrγr) Relativistic Momentum 959 1066 1066H Hour Glass Form Factor 0.65 0.69 0.72

L Peak Luminosity (1032 cm-2 sec-1) 0.19 0.8 2.0

∫L Integrated Luminosity (pb-1/week) 3.8 17 40NIR Number of interaction Regions 2 2 2

The quantity NaB (called the stack size) in equation (2.1.1) is just the total antiprotonintensity injected into the Tevatron Collider, independent of the number of bunches thatcharge is divided into. Note that the luminosity grows proportionally with this number,the fact which is the basis of the luminosity improvement generated by the Recycler ring.This relationship between luminosity and antiproton availability is due to the fact that theproton intensity is limited. The limit on the proton intensity comes from the observation that the maximumallowable total antiproton linear beam-beam tune shift from all bunch crossings with theproton bunches is approximately 0.026. The equation relating this maximum antiprotontotal tune shift ξmax and the proton intensity is

ξmax = ro4π

Np

εnpNIR . (2.1.4)

The quantity ro is the classical radius of the proton (1.53x10-18 m). The number ofinteraction regions NIR is at a minimum equal to the number of high energy physics


detectors operating in the collider. Plugging this equation for the tune shift into theequation for luminosity per interaction region (2.1.1) yields the result

L =NaB( )

NIR β*2ξmax fo 6βrγ r( )

ro 1 + εnaεnp

Hβ*

12 σsp

2 + σsa2( )

, (2.1.5)

where the factors whose values can be significantly modified appear in the left fraction onthe right hand side of the equation. The emittances of the protons and antiprotons can bechanged, but the ratio of the proton to antiproton emittances is always near unity due tononlinear beam dynamics concerns. Therefore, reducing the emittances of the beams isnot helpful once the beam-beam limit has been reached.

Even though β* can be changed, eventually the length of the bunch and the sensitivityof the lattice to errors in low-β quadrupole strengths limits the extent to which β* can bereduced. The number of interaction regions is chosen by the high energy physicscommunity. Note that for a uniform β* in all detectors, the sum of the luminosityavailable in the Tevatron Collider at all interaction regions is conserved as the number ofinteraction regions is changed.

Tevatron Collider Luminosity

Antiproton Stack Intensity

Time

Figure 2.1.1: Sketch of antiproton stacking during Tevatron Colliderstores. At the beginning of each store some of the stacked antiprotons aredelivered to the Tevatron. During the store those antiprotons arereplenished via continuous Main Injector operations.

2.1.2. Antiproton Stacking

As demonstrated in the previous section, the dominant limitation to high luminosityoperations in proton-antiproton colliders is the availability of bright (high current and lowemittance) antiproton beams. Antiprotons are produced by aiming 120 GeV protons from


the Main Injector onto a metallic target. For every million protons, approximately 15antiprotons are captured, cooled, and stored for future use. Because of this very smallyield, antiproton production must occur continuously while the Tevatron is storing beamand creating proton-antiproton collisions for high energy physicists.

While the Tevatron is storing beam at an energy of 1 TeV, the Main Injector iscontinuously cycling. Every ~2 seconds the Main Injector accelerates protons from akinetic energy of 8 GeV to the required 120 GeV for antiproton production. The 8 GeVkinetic energy antiprotons from the target are cooled and stored (stacked) in theDebuncher and Accumulator rings. As the Tevatron stores the beam the luminositydecreases due to particle loss and emittance growth. Therefore, a certain antiprotonstacking rate is required to keep the Tevatron operating at a determined typical peakluminosity level. Figure 2.1.1 contains a sketch of the Tevatron luminosity andantiproton stack size during collider operations.

2.1.3. Luminosity Evolution

The evolution of the luminosity and antiproton intensity during a Tevatron Colliderstore is determined by the luminosity itself, intrabeam scattering, external transverse andlongitudinal emittance growth mechanisms, and the length of the store. The parameterswhich depend on luminosity itself are the proton and antiproton intensity lifetimes. Thecentral purpose of the Tevatron Collider is to collide protons and antiprotons, using themup at the rate of

Rlost = NIR L σlost , (2.1.6)

where σlost is the 78 mb cross-section [E811 collaboration] for losing protons andantiprotons due to both inelastic and large elastic interactions and NIR is the number ofinteraction regions in the Collider. The proton and antiproton intensity lifetimes due tothis mechanism are calculated using the equation

τLp,La =Np,a B

Rlost . (2.1.7)

Another limit to beam intensity lifetime is the residual vacuum in the Tevatron. Thevacuum intensity lifetime τvac is approximately 200 hours at the present time.

The other parameters which vary during a store are the bunch length and thetransverse emittance. One mechanism observed to induce emittance growth during astore was external noise. When noise driven coherent betatron and synchrotronoscillations decohere due to nonlinearities, a constant emittance growth rate isestablished. Over the years this emittance growth rate has been lowered to a fairlyinsignificant level of 0.3 π mmmr/hr 95% normalized transversely and 0.01 eV-sec/hr95% normalized longitudinally. Another mechanism is multiple Coulomb scatteringagainst the residual molecules in the vacuum chamber.

The growth times of the transverse and longitudinal emittances due to intrabeamscattering in the Tevatron are described by the equations [D. Finley, TM-1646 (1989)]


τεp = 0.0546x1010

NP

ε nP

2.24 AP0.68 , (2.1.8)

τAp = 0.1036x1010

NP

ε nP1.24 AP

1.68 , (2.1.9)

where εnp and Ap are the normalized 95% transverse (π mmmr) and longitudinal (eV-sec)emittances of the protons and the times are in hours. The antiproton growth times arecalculated similarly. This equation assumes the Tevatron Collider lattice and an RFvoltage of 1 MV/turn.

By including all of the above effects into a calculation of the evolution of theluminosity and beam properties during a collider beam store, predictions can be made. Inorder to confirm that the factors affecting luminosity evolution are understood, thesecalculations were applied to the recently completed collider Run I. This model isquantitatively in agreement in all beam parameters in all measured stores in whichcomparisons have been performed. Therefore, it is with confidence that predictions ofRun II performance are presented below.

Time (hours)

Lum

inos

ity (

E30

cm

-2 s

-1)

020406080

100120140160180200

0 4 8 12

Figure 2.1.2: Prediction of the time evolution of luminosity during aTevatron Collider store during Run II with the Recycler ring.

The prediction of Run II luminosity evolution appears in figure 2.1.2. The luminositydrops by a factor of two in about six hours. The next factor of two drop requires morethan an additional 12 hours. The principal reason for this increase in the luminositylifetime with elapsed time in the store is intrabeam scattering. The transverse emittancetime evolution of both the protons and antiprotons are shown in figure 2.1.3. Theemittance growth rates are initially steep and decrease with time in the store. In addition,the longitudinal emittance of the protons and antiprotons also grow during a store due tointrabeam scattering. The predictions for this effect of intrabeam scattering are displayedin figure 2.1.4.


The longitudinal emittance of the antiproton bunches in figure 2.1.4 start out smalldue to the fact that the Recycler ring is capable of forming the required intensity buncheswithout the use of coalescing. The 11 proton and antiproton bunches before coalescing inthe present collider run have a longitudinal emittance of approximately 0.2 eV-s each.Instead of the expected longitudinal emittance of 2.2 eV-s for the coalesced bunch, theinitial emittance ends up as ~3 eV-sec. The process of coalescing dilutes the longitudinalemittance by approximately 50%.

Time (hours)

Em

ittan

ce (π

mm

mr)

0

5

10

15

20

25

30

0 4 8 12

Figure 2.1.3: Predictions of the proton (upper) and antiproton (lower)transverse 95% invariant emittances as a function of time during Run IIwith the Recycler ring.

Time (hours)

Bun

ch A

rea

(eV

-s)

0

2

4

6

8

0 4 8 12

Figure 2.1.4: Predictions of the proton (upper) and antiproton (lower)longitudinal 95% invariant emittances as a function of time during Run IIwith the Recycler ring.

For 36x36 bunch operations, the total longitudinal emittance of the antiprotons storedin the Recycler ring must be partitioned into 36 equal portions. The total invariant 95%longitudinal emittance of the Recycler ring Ar is


Ar = 4 To σe , (2.1.10)

where To is the revolution period of the Recycler and σe is the rms energy spread. Giventhe Main Injector longitudinal admittance of 0.5 eV-s (at transition crossing) for a singlebunch in a 53 MHz RF bucket, the total Recycler longitudinal emittance must be less than18 eV-sec. For reference, this 18 eV-sec emittance corresponds to an rms energy spreadof 0.4 MeV, or a fractional energy spread of approximately 5x10-5. Because thestochastic cooling system cannot generate such small longitudinal emittances in thepresence of the expected intrabeam scattering growth rates, the 2.5 MHz RF systemnormally used for coalescing will be used to accelerate and decelerate the beam throughtransition. The backup plan is to use the traditional coalescing manipulation, which hasthe disadvantages of larger final longitudinal emittance and lower charge efficiency.

Time (hours)

Prot

ons/

Bun

ch (

E9)

0

50

100

150

200

250

300

0 4 8 12

Figure 2.1.5: Prediction of the proton bunch intensity as a function of timeduring Run II with the Recycler ring.

Time (hours)

Ant

ipro

tons

/Bun

ch (

E9)

0

10

20

30

40

50

60

70

0 4 8 12

Figure 2.1.6: Prediction of the antiproton bunch intensity as a function oftime during Run II with the Recycler.


The time evolution of the proton and antiproton bunch intensities are shown in figures2.1.5 and 2.1.6. As expected, because the rate of particle loss for both beams is equal andthe antiproton total intensity is much lower than that of the protons, the proton intensitylifetime is much longer than the antiproton lifetime. The third major benefit of theRecycler ring is the ability to recycle antiprotons remaining at the end of a store. In orderto assess the benefit of antiproton recycling, the percentage of the original antiprotonintensity remaining at the end of the store is critical. The next task is to consider theoptimum length of a store.

2.1.4. Optimum Store Length

The goal of the Tevatron Collider is to integrate luminosity at the highest ratepossible. In order to achieve this goal, high initial luminosities, long luminosity lifetimes,and high stacking rates are required. The store length Ts is also equal to the timeavailable for stacking between injections. The filling time Tf is determined by a numberof factors not relevant to this discussion. In present operations using the Accumulator tostack antiprotons the time evolution of the luminosity and antiproton stack size have thedependencies sketched in figure 2.1.7. The total Tevatron Collider cycle time Tc is thesum of the store time and the fill time.

L

Na

Ts

Tf

0 Tc t

t

Figure 2.1.7: Sketch of the time dependence of luminosity andaccumulated antiproton stack intensity during Collider Run I. The storetime Ts plus the fill time Tf equals the total collider cycle time of Tc.

To maximize the rate at which integrated luminosity is delivered, it is necessary tomaximize the average luminosity <L>, which is defined as

L = 1Ts + Tf

L(t)dt

0

Ts

∫ . (2.1.11)


Because antiproton recycling is assumed, Ts plus the deceleration efficiency partiallydetermine the initial number of available antiprotons. The recycled antiprotons are notimmediately recooled, but stored and cooled for an entire Tevatron Collider store. Themodel used to predict the luminosity and other beam parameters during Run II operationsalso generates the integrated luminosity vs. time during a store. It assumes steady stateoperations with no Collider failures. By allowing the store duration to be the independentvariable, the dependence of the average luminosity on store length for a number ofchoices for the fill time is plotted in figure 2.1.8. As expected, shorter fill timescorrespond to high average luminosities and shorter optimum store lengths. Even thoughfill times of one half hour are possible, it is more likely that fill times around 1 hour willbe operationally feasible. At that choice of fill time, there is only a 10% difference inaverage luminosity between the optimum of 3.5 hours and 8 hours. A store length of 7hours will be used as the reference store length for discussions below.

Store Duration (hrs)

Ave

rage

Lum

inos

ity

(p

b-1/

hr)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 4 8 12

Figure 2.1.8: Prediction of the average luminosity vs. store duration for filltimes of 0.5 (top), 1.0, 1.5, and 2.0 (bottom) hours. The longer the filltime, the longer is the optimum store duration. The above calculationassumes the existence of the Recycler during Run II.

The main impact of the store length is the antiproton stacking rate required tomaintain the design luminosity of 2x1032 cm-2 sec-1 during Run II. In order tounderstand how the curve in figure 2.1.9 describing the required stacking rate vs. storeduration was generated, refer to table 2.1.2.

The values in the rows labeled "Antiprotons at End of Store" and "IntegratedLuminosity" were generated by the luminosity evolution calculations described above.The fill time for the MI and the MI with the Recycler ring are estimates. The MainInjector fill time is longer since without recycling the optimum store length is longer,making fill time less critical to average luminosity and putting less pressure on effortsaimed at shortening the injection time. The acceleration efficiency is the same as thevalue of 90% chosen in the original Main Injector design. The deceleration efficiency of80% is basically the acceleration efficiency plus a factor due to the initially novel natureof this operation. Plugging in all of these parameter values, one can generate thesubsequent numbers.



Req

uire

d St

acki

ng R

ate

(E10

/hr)

05

10152025303540

0 4 8 12

Figure 2.1.9: Prediction of the stacking rate required to achieve repeatedstores at the peak luminosity of 2x1032 cm-2 s-1.

Table 2.1.2: Parameters which describe the effect of recycling antiprotonson antiproton stacking and average luminosity during Run II.Comparisons are made with Run I operations (without both the MainInjector and the Recycler).

Parameter Run I MI only RecyclerStore Duration Ts (hr) 12 12 7Injection Time Tf (hr) 2.5 1 1Antiprotons at End of Store 73% 65% 78%Deceleration Efficiency 0% 0% 80%Acceleration Efficiency 75% 90% 90%Integrated Luminosity (pb-1/store) 0.56 2.9 3.4

Required Usable Stack (1010) 48 144 264

Antiprotons Recycled (1010) 0 0 148

New Antiprotons Stacked (1010) 48 144 116

Required Stacking Rate (1010/hr) 4 12 17Average Luminosity (pb-1/hr) 0.04 0.21 0.43Store Hours Needed to Achieve theSnowmass Criterion BetweenIntegrated and Peak Luminosity

98(typical)

101 93

The required usable stack is simply the initial total antiproton intensity in theTevatron divided by the acceleration efficiency. In other words, it is the number ofantiprotons which must be extracted from the Accumulator now or the Recycler in thefuture in order to attain the number of antiprotons called for in table 2.1.1. The numberof antiprotons recycled is the initial antiproton intensity times the fraction of antiprotonsremaining at the end of the store times the deceleration efficiency. The number ofantiprotons stacked is simply the difference between the required stack size and thenumber of antiprotons recycled. In the case of Run II with the Recycler, recycling


contributes more than a factor of two to the luminosity. The stacking rate is just thenumber of stacked antiprotons divided by the store duration.

2.1.5. Luminosity Leveling

At a given luminosity, the maximum number of interactions per crossing which theHEP detectors can absorb while still performing physics research determines the numberof bunches per beam. Table 2.1.3 contains a summary of the average number ofinteraction per crossing for Run I and anticipated with the Main Injector alone and withthe addition of the Recycler. The purpose of the Tevatron Collider is to record usefulHEP interactions on tape at the fastest possible rate. From the perspective of anaccelerator physicist, this requires the delivery of integrated luminosity at the fastest ratepossible. In other words, the average luminosity in equation 2.1.11 must be maximized.From the perspective of an HEP physicist, a high average luminosity is desired only if thenumber of interactions per crossing is at a "reasonable" level. Too many interactions in agiven crossing increases the chances of mistaking tracks associated with a given vertex,thereby decreasing trigger and off-line analysis efficiencies. The problem is that the word"reasonable' is very soft, depending on the type of particle tracking and identificationrequired for a given class of measurements. The general consensus is an average numberof interactions per crossing below 5-6 are probably reasonable for Run II.

Table 2.1.3: Average number of interactions per crossing at each HEPdetectors at the beginning of stores for the same three scenariossummarized in tables 2.1.1 and 2.1.2. These rates occur at the peakluminosities listed in table 2.1.1.

Parameter Run I MI only RecyclerAverage Number of Interactionsper Crossing (@ 49 mb) 3.2 2.4 5.7

One method for controlling the interactions per crossing problem while stilldelivering a high average luminosity is called luminosity leveling. In this plan the peakluminosity at the beginning of a store is sacrificed in order to maintain a stable averageluminosity for a longer period of time. The method for achieving this luminosity profilecalls for slowly decreasing the β* at the interaction period, starting at a larger initialvalue. For example, in figure 2.1.2 a constant value of β* = 35 cm was assumed. Usingthe same simulation of Tevatron Collider performance, the time dependence for β*

shown in figure 2.1.10 was assumed.Of course the primary effect of this continuous low beta squeeze is on the luminosity,

shown in figure 2.1.11. In this example the peak luminosity was decrease by almost afactor of two, bringing the average number of interactions per crossing down to the peakvalue experienced in Run I. The β* is decreased until the minimum value of 35 cm isreached. Because the low beta squeeze has no effect on the beam sizes around the ring,the emittance growth mechanisms are not affected. In addition, with the exception ofparticle losses due to these interaction region collisions, the beam intensity evolution isalso unaffected. In fact, for the luminosity leveling example investigated here the


evolution of emittances and intensities are identical to those shown in figures 2.1.3through 2.1.5.

Time (hours)

ß* (

cm)

0102030405060708090

0 4 8 12

Figure 2.1.10: Continuous low beta squeeze during a Tevatron Colliderstore which produces a constant luminosity. The squeeze ends at 35 cm,which is considered the minimum for Run II.

Time (hours)

Lum

inos

ity (

E30

cm

-2 s

-1)

020406080

100120140160180200

0 4 8 12

Figure 2.1.11: Luminosity as a function of time for the same initial valuesof beam intensity and emittance, but employing the continuous low betasqueeze to level the luminosity.

The only noticeable change is in the antiproton intensity lifetime, which is dominatedby the rate of proton-antiproton collisions. The antiproton intensity evolution with timeis shown in figure 2.1.12. It is this improvement in antiproton lifetime which explainswhy the luminosity curve in figure 2.1.10 is higher than the constant β* curve in figure2.1.1 after 6 hours.

Since the luminosity lifetime is improved, the loss in average luminosity is not assevere as might at first be expected. As shown in figure 2.1.13, the biggest impact is topush the optimum store length out by 2-3x to values which were typical in Run I. In fact,


assuming a 1 hour injection time, the optimum store length is 10-11 hours. On the otherhand, comparing with figure 2.1.8, the optimum average luminosity decreased by 25%.

Time (hours)

Ant

ipro

tons

/Bun

ch (

E9)

0

10

20

30

40

50

60

70

0 4 8 12

Figure 2.1.12: Time evolution of the antiproton intensity per bunch whenluminosity leveling is employed. At the end of 8 hours there areapproximately 10% more antiprotons in the Tevatron as compared withthe case of constant β*.


Ave

rage

Lum

inos

ity

(p

b-1/

hr)

0

0.1

0.2

0.3

0.4

0 4 8 12

Figure 2.1.13: Prediction of the average luminosity as a function of storeduration for fill times of 0.5 (top), 1.0, 1.5, and 2.0 (bottom) hours. In thisexample luminosity leveling in which the peak luminosity is decreased bya factor of 2 is assumed.

The impact of luminosity leveling on the stacking rate required to achieve a steadystate condition of repetitive stores is small but positive. Displayed in figure 2.1.14, therequired stacking rate is slightly smaller for all choices of store length. But what if thestacking rate does reach it's design goal of 16x1010 antiprotons/hour?



Req

uire

d St

acki

ng R

ate

(E10

/hr)

05

10152025303540

0 4 8 12

Figure 2.1.14: Prediction of the stacking rate required to achieve steadystate luminosity performance assuming luminosity leveling. As found inthe case of constant β*, longer store lengths mean that a lower antiprotonstacking rate still produces the same peak luminosity.

This was the stacking rate needed to achieve the 7 hour store lengths assumed in thecase of constant β*, so it is a reasonable assumption. At the same time, relax theinteraction per crossing criterion and require that the optimum average luminosity be thesame as the constant β* case. In this case the initial antiproton intensity per bunch in theTevatron increases from 66x109 to 100x109, the initial luminosity is 1.3x1032 cm-2 sec-1,and the peak average number of interactions per crossing is the manageable value of 3.7!

Time (hours)

ß* (

cm)

0102030405060708090

100

0 4 8 12

Figure 2.1.15: Continuous low beta squeeze which generates a constantluminosity at 65% of peak with an antiproton stacking rate of16x1010 antiprotons/hour.

Figure 2.1.15 shows the continuous low beta squeeze needed to maintain a constantluminosity at the higher initial antiproton intensity. Since the goal is to end up with the


same optimum average luminosity, the peak luminosity shown in figure 2.1.6 is 65% ofthe peak design luminosity of 2x1030 cm-2 sec-1 in the absence of luminosity leveling.

Time (hours)

Lum

inos

ity (

E30

cm

-2 s

-1)

020406080

100120140160180200

0 4 8 12

Figure 2.1.16: Prediction of the time dependence of Run II luminosityassuming luminosity leveling at 65% of peak with an antiproton stackingrate of 16x1010 antiprotons/hour at an optimum store length of 11 hours.

Time (hours)

Ant

ipro

tons

/Bun

ch (

E9)

0102030405060708090

100

0 4 8 12

Figure 2.1.17: Prediction of the time dependence of the antiprotonintensity/bunch assuming luminosity leveling at 65% of peak with anantiproton stacking rate of 16x1010 antiprotons/hour at an optimum storelength of 11 hours.

Because there are more antiprotons and a lower peak luminosity, the antiprotonintensity lifetime is considerably longer than in the case of no luminosity leveling (seefigure 2.1.17). So even for double the store length the percentage of antiprotons left atthe end of the store is the same. But because the antiproton intensity is higher for longer,the transverse and longitudinal emittance growth of the antiprotons are also larger. Theupdated emittance evolution curves are displayed in figure 2.1.18 and 2.1.19. Note thatbecause of the greater growth rates and the longer stores, the recycled antiprotons will


have transverse emittances approaching 25 π mmmr and longitudinal emittances of4 eV-sec.

Time (hours)

Em

ittan

ce (π

mm

mr)

0

5

10

15

20

25

30

0 4 8 12

Figure 2.1.18: Prediction of the time dependence of the proton (top) andantiproton (bottom) transverse normalized 95% emittance assumingluminosity leveling at 65% of peak with an antiproton stacking rate of16x1010 antiprotons/hour at an optimum store length of 11 hours.

Time (hours)

Bun

ch A

rea

(eV

-s)

0

2

4

6

8

0 4 8 12

Figure 2.1.19: Prediction of the time dependence of the proton (top) andantiproton (bottom) longitudinal normalized 95% emittance assumingluminosity leveling at 65% of peak with an antiproton stacking rate of16x1010 antiprotons/hour at an optimum store length of 11 hours.

By design, the average luminosity (figure 2.1.20) and stacking rate (figure 2.1.21) at astore length of 11 hours is equal to the constant β* case at a store length of 7 hours.There are some advantages with this luminosity leveling scenario beyond the argumentsconcerning interactions per crossing. For example, the longer store lengths reduces thesensitivity to unanticipated increases in the fill time. It also gives the Recycler more timeto cool the recycled antiprotons.



Ave

rage

Lum

inos

ity

(p

b-1/

hr)

0

0.1

0.2

0.3

0.4

0.5

0 4 8 12

Figure 2.1.20: Average luminosity assuming luminosity leveling at 65%of peak with an antiproton stacking rate of 16x1010 antiprotons/hour at anoptimum store length of 11 hours. The four curves are for injection timesof 0.5 (top), 1.0, 1.5, and 2.0 (bottom) hours.


Req

uire

d St

acki

ng R

ate

(E10

/hr)

05

10152025303540

0 4 8 12

Figure 2.1.21: Required antiproton stacking rate to support luminosityleveling at 65% of peak with an antiproton stacking rate of16x1010 antiprotons/hour at an optimum store length of 11 hours.

2.1.6. Antiproton Recycling

In order to achieve the luminosity goal of Fermi III with the Recycler, the proton andantiproton beams will have to be extracted from the Tevatron. This section is a review ofthe beam parameter values and issues associated with the transfers from TevatronCollider end-of-store to storage in the Recycler.

The process of recycling starts in the Tevatron at 1 TeV in the low-β latticeconfiguration. The first step is to eliminate the protons. Computer controlled collimatorsare used to scrape away the protons (which are on one strand of the separated orbit helix)without intercepting antiprotons and without quenching Tevatron magnets. It is


anticipated that once some experience has been gain that this operation can take as littletime as 5 minutes.

Once the protons are eliminated, the electrostatic separators can be turned off,dramatically increasing the available aperture for the larger emittance antiprotons. Theantiprotons can then be decelerated while remaining in the low-β lattice, or the low-βlattice can be unsqueezed back into the injection lattice. Changing β* from its injectionvalue to 35 cm and back to its injection value has already been performed at 900 GeV.The resulting tune change was only 0.004 from the value before reducing β*. Thedecision of whether or not to unsqueeze from the low-β lattice should depend on whichapproach provides the brightest antiproton bunches to the Main Injector.

The maximum deceleration rate expected is 16 GeV/sec which is the acceleration rateused for Collider Run I. This acceleration rate was chosen so that acceleration would stillbe possible with a single RF station non-operational. If the deceleration ramp isconstructed to be a mirror image of the acceleration ramp from Collider Run I, the RFsystem can still produce a 3 eV-sec bucket with a missing station. The regulation of themain power supply and low beta quadrupole systems is not a problem. The current mainpower supply regulation error coming out of flattop is about 100 mA, about a factor of 2higher than the error at the start of ramp. Regulation parameters can be adjusted to try toimprove this regulation. With a single beam in the machine, this regulation error is not aproblem. With a deceleration ramp that mirrors the acceleration ramp, the low-βquadrupole power supplies will need no modification. If the rate of deceleration isincreased near the injection energy, four of the power supplies will need to be given theability to invert.

The waveform generators used to control most Tevatron power supplies have enoughcapability to produce the additional ramps needed. The correction dipoles, however, havean older waveform generator that may need to be reloaded for the deceleration process.This will be operationally awkward, but is not technically difficult. Replacement of thesegenerators with newer models is under present consideration.

The biggest challenge will be correctly compensating for the changing sextupolecomponent in the main dipoles. Some magnet measurements have been made to analyzethese fields so that compensation ramps can be calculated. The expected current neededfrom the chromaticity sextupoles is well within the capabilities of the existing circuits.The exact shape of the deceleration ramp will be finalized after all results of the magnetmeasurements are available.

The antiprotons will be decelerated to a DC energy of 150 GeV. The exact number ofbunches transferred at a time will depend on the proton injection kicker used. It is likelythat this kicker will have a flattop long enough to transfer 4 bunches at a time. Nine MainInjector cycles would then be needed to transfer all antiproton bunches to the Recycler.The Tevatron needs to be at 150 GeV for no more than 3 minutes to complete thetransfers to the Main Injector. The main issue at this point will be compensating the timevarying sextupole fields in the Tevatron during this period. The exact scheme for thiswill be determined after more Tevatron magnet measurements are complete.

The transverse aperture in the Tevatron at 150 GeV is approximately 25 π mmmr withthe electrostatic separators turned on. Since the separators are off during recycling, thetransverse aperture is even larger and once measured at approximately 40 π mmmr.


Therefore, since the antiprotons are expected to increase in emittance to less than25 π mmmr, no problems with transverse aperture are anticipated. In table 2.1.4 thelongitudinal aperture of the Tevatron is explored. At 150 GeV the maximum RF voltageis 1 MV. This is also the maximum voltage at the flattop energy of 1 TeV. Note that thebucket area decreases from 11 eV-sec to 4.2 eV-sec as the antiprotons are decelerated.This bucket area is sufficient to accommodate the 4 eV-sec bunches expected at the endof a store, even if luminosity leveling is employed.

Table 2.1.4: Longitudinal parameters relevant to antiproton deceleration inthe Tevatron during the recycling process.

Parameter Tevatron FT Tevatron InjBeam Kinetic Energy (GeV) 1000 150RF Voltage (MV) 1 1RF Frequency (MHz) 53 53Momentum Compaction Factor 0.0028 0.0028RF Bucket Half Length (nsec) 9.4 9.4RF Bucket Half Height (MeV) 450 175Invariant RF Bucket Area (eV-sec) 11 4.2Synchrotron Frequency (Hz) 34 87Invariant 95% Longitudinal Emittance (eV-sec) 3 3Matched RMS Bunch Length (nsec) 1.5 2.3Matched RMS Energy Spread (MeV) 110 68Fractional RMS Momentum Spread (%) 0.011 0.045Ratio of Emittance to Bucket Area 0.28 0.71

The Main Injector has a design transverse aperture of 40 π mmmr. The Recycler ringhas been chosen to have the same aperture. Therefore, at no point in the remainder of therecycling process is transverse aperture envisioned to cause any difficulties, evenassuming 1-2 π mmmr of invariant emittance growth per transfer between accelerators.

Since the Tevatron and the Main Injector have different circumferences, the RFvoltage in each ring at Tevatron to Main Injector transfer must be different in order togenerate matched RF buckets. Otherwise, longitudinal emittance growth will occur justafter the transfer. As can be seen in table 2.1.5, a Main Injector RF voltage of 0.4 MVgenerates a bucket height and area equal to a Tevatron voltage of 1.0 MV. Based onpresent operational experience, the transfer between the Tevatron and Main Injectorshould only increase the already large bunch area by approximately 0.1-0.2 eV-sec.

The maximum 53 MHz RF voltage in the Main Injector is approximately 4 MV. Thisvoltage is required for fast deceleration when the synchronous phase must be limited inorder to maintain bucket area. In table 2.1.5 deceleration in the Main Injector to 25 GeVusing the standard 53 MHz RF system is described. The energy of 25 GeV is far enoughabove transition that longitudinal beam dynamics are not distorted by the strong energydependence of the momentum compaction factor near transition.


Table 2.1.5: Longitudinal parameters relevant to antiproton deceleration inthe Main Injector during the recycling process. This table describes thestandard deceleration phase from Tevatron transfer down to 25 GeV, justbefore transition crossing.

Parameter MI Flattop MI 25 GeVBeam Kinetic Energy (GeV) 150 25RF Voltage (MV) 0.4 1.2RF Frequency (MHz) 53 53Momentum Compaction Factor 0.0021 0.0008RF Bucket Half Length (nsec) 9.4 9.4RF Bucket Half Height (MeV) 178 206Invariant RF Bucket Area (eV-sec) 4.2 4.9Synchrotron Frequency (Hz) 65 168Invariant 95% Longitudinal Emittance (eV-sec) 4 4Matched RMS Bunch Length (nsec) 2.7 2.5Matched RMS Energy Spread (MeV) 80 85Fractional RMS Momentum Spread (%) 0.053 0.33Ratio of Emittance to Bucket Area 0.93 0.81

The problem with transition crossing is that the longitudinal admittance hits itsminimum at 0.5 eV-sec. This aperture limitation is caused by the normal increase inmomentum spread (and conjugate decrease in the bunch length) during transitioncrossing. Assuming a nominal longitudinal emittance of 4 eV-sec, it is clear thatantiproton recycling via the 53 MHz RF system alone is not possible. But if the RFfrequency were decreased by a factor of 8 or more, then the matched bunch length wouldbe longer and momentum spread decreased correspondingly. Since the Main Injectorcontains a 2.5 MHz RF system, it is natural to investigate using that system for transitioncrossing and the remaining deceleration to the base kinetic energy of 8 GeV.

The transition from one RF system to the other can take place relatively easily byturning on the 2.5 MHz system and then adiabatically lowering the 53 MHz voltage tozero. The maximum sustainable voltage in the 2.5 MHz system is 60 kV. Table 2.1.6contains the parameter values for transfer to the 2.5 MHz system. Once the transfer hastaken place, the antiprotons can be decelerated at a rate of the peak voltage times the sineof the synchronous phase angle. Assuming a phase angle of 53°, the beam can bedecelerated at a rate of 48 keV/turn, or 4.25 GeV/sec. At this rate it takes 4 seconds todecelerate the beam down to a kinetic energy of 8 GeV.

In order to deliver the smallest possible momentum spread beam to the Recycler, at8 GeV the RF voltage is reduced adiabatically until the bunch longitudinal emittanceequals the bucket area. Table 2.1.7 contains the longitudinal parameters just beforetransfer to the Recycler. The beam delivered to the Recycler has an energy spread lessthan 4 MeV, even for the large longitudinal emittance of 4 eV-sec.

The act of transition crossing has been simulated using the ESME program. Figure2.1.22 contains the resultant phase space distribution of a 3 eV-sec bunch after crossingtransition with only an instantaneous RF phase change. No special RF or gamma-t jumpmanipulations are involved. Note that the longitudinal emittance grew by approximately10%, and no test particles out of the original 1000 were lost. The case of 4 eV-sec


transition crossing was also studied with ESME. The result is that for an identicaldeceleration as in the previous 3 eV-sec case, the longitudinal emittance is diluted to5.1 eV-sec, which represents a 25% growth. On the other hand, no beam loss wasobserved. Repeating the 4 eV-sec transition crossing simulation but this time with agamma-t jump, the longitudinal emittance dilution was reduced to less than 10%.

Table 2.1.6: Longitudinal parameters relevant to antiproton deceleration inthe Main Injector during the recycling process. This table documents thetransfer of RF systems to the 2.5 MHz system for deceleration throughtransition to a kinetic energy of 8 GeV.

Parameter RF HandoffBeam Kinetic Energy (GeV) 25RF Voltage (kV) 60RF Frequency (MHz) 2.5Momentum Compaction Factor 0.0008RF Bucket Half Length (nsec) 198RF Bucket Half Height (MeV) 211Invariant RF Bucket Area (eV-sec) 106Synchrotron Frequency (Hz) 8.2Invariant 95% Longitudinal Emittance (eV-sec) 4Matched RMS Bunch Length (nsec) 11.2Matched RMS Energy Spread (MeV) 18.8Fractional RMS Momentum Spread (%) 0.073Ratio of Emittance to Bucket Area 0.037

Table 2.1.7: Longitudinal parameters relevant to antiproton deceleration inthe Main Injector during the recycling process. This table documents theremaining deceleration to the kinetic energy of 8 GeV and transfer into therectangular barrier bucket RF system of the Recycler ring, where theenergy spread must be minimized.

Parameter MI @ 8 GeVBeam Kinetic Energy (GeV) 8RF Voltage (kV) 2.8RF Frequency (MHz) 2.5Momentum Compaction Factor -0.0089RF Bucket Half Length (nsec) 198RF Bucket Half Height (MeV) 8.0Invariant RF Bucket Area (eV-sec) 4.04Synchrotron Frequency (Hz) 10Invariant 95% Longitudinal Emittance (eV-sec) 4Matched RMS Bunch Length (nsec) 58Matched RMS Energy Spread (MeV) 3.7Fractional RMS Momentum Spread (%) 0.041Ratio of Emittance to Bucket Area 0.99


Figure 2.1.22:Simulation of longitudinal phase space of a 3 eV-sec bunchafter crossing transition with a simple RF phase change and no gamma-tjump.

The recycled antiproton beam in the Tevatron are handled as 9 batches eachcomposed of 4 bunches spaced at a 2.5 MHz frequency. The entire recycling processrepeats the Main Injector deceleration and transfer process 9 times, once per batch. Thenext issue to address is how the transfers and RF manipulations are handled during therecycling process between the Main Injector and the Recycler.

(a)

(b)

Figure 2.1.23: Full ring phase space sketches of the initial steps ofantiproton recycling in the Recycler. In the top drawing (a) the cooledbeam starts off basically unbunched (unless an azimuthal gap is necessaryfor ion clearing reasons). In the bottom drawing (b) a rectangular barriervoltage system adiabatically squeezes the beam into a small fraction of thecircumference.


In the remainder of this discussion luminosity leveling is not assumed. Whenluminosity leveling is included some quantitative values may change, but the qualitativeflavor of the operations and concerns remains unchanged.

When the entire recycling process starts, the Recycler already contains 264x1010

antiprotons (116x1010 newly stacked, 148x1010 from the recycling process of theprevious store). Given calculations of intrabeam scattering and the choice of stochasticmomentum cooling system, the longitudinal emittance is cooled to approximately54 eV-sec, which according to equation (2.1.10) corresponds to a fully occupied ring withan rms energy spread of 1.2 MeV (see figure 2.1.23a). The first step is to generate abarrier bucket [J.E. Griffin, C. Ankenbrandt, J.A. MacLachlan, and A. Moretti, "IsolatedBucket RF Systems in the Fermilab Antiproton Facility", IEEE Trans. Nucl. Sci. NS-30,3502 (1983)] voltage waveform which constrains the cooled beam distribution to onequarter of the circumference, as shown in figure 2.1.23b. In figure 2.1.24 the phase spacecapture bucket generated by a pair of rectangular voltage pulses is shown. Because of theintrinsic wide bandwidth of modern power amplifiers, rectangular pulses are desirable forgenerating the largest bucket height for the smallest pulse width and voltage. The buckethalf height ∆E1/2 given a pulse voltage of Vo, a beam total energy of Eo, a pulse width ofT, a revolution period of To, and a momentum compaction factor η is

∆E1/2 = TTo

2βr2

ηeVo Eo . (2.1.12)

Barrier Voltageε

τ∆E1/2

T

Figure 2.1.24: Phase space sketch associated with a rectangular barrierbucket accelerating voltage system. Inside the voltage pulse the trajectoryof energy vs. longitudinal position is quadratic.

Assuming that one wants to longitudinally compress this beam distribution so that themomentum span of the bunch grows out to the momentum aperture of the stochasticcooling systems, the rms momentum spread has grown to approximately 4.8 MeV andcharge length has been compressed into 1/4 of the ring circumference. Assuming ±2 σeof bucket height to constrain most of the beam to that portion of the circumference,table 2.1.8 describes the required voltage and pulse length necessary to produce theminimum bucket height. The final beam distribution length is approximately 2.8 µsec outof 11.2 µsec, so 8.4 µsec of free circumference is available for the recycling process.


Table 2.1.8: Parameters which produce the minimum bucket heightnecessary to constrain a beam distribution with an rms energy spread of4.5 MeV.

Parameter σe=4.5 MeVBeam Total Energy (GeV) 8.938Relativistic Velocity 0.9945RF Voltage (kV) 1.2RF Pulse Length (µsec) 0.5Momentum Compaction Factor -0.008683Revolution Period (µsec) 11.2RF Bucket Half Height (MeV) 10

(a)

(b)

(c)

(d)

(e)

Figure 2.1.25: Recycling of antiproton batches from the Main Injector.The leftmost charge distribution is always the cooled antiprotons. Theshown Recycler injection kicker waveform has a rise-time and fall-time of1 µsec. The recycling process never requires more than 3 pairs of barriervoltage pulses.


Figure 2.1.26: Simulation result of the adiabatic debunching of the2.5 MHz bunch structure into a barrier bucket. In this figure the initialdistribution with an rms fractional momentum spread of 0.00033 is shown.

Figure 2.1.26: Simulation result of the adiabatic debunching of the2.5 MHz bunch structure into a barrier bucket. In this figure the finaldistribution with an rms fractional momentum spread of 0.00020 is shown.The 2.5 MHz sinusoidal matching waveform was reduced in voltagelinearly in 1 second.


The transfers of bunches from each batch from the Main Injector to the Recycler ringis performed 4 bunches at a time. The length of a series of 4 recycled collider bunches inthe Recycler ring just after transfer is 1.6 µsec. According to table 2.1.7 the rms energyspread of this distribution at 3 eV-sec per bunch is 2.8 MeV. A sketch of this injection inlongitudinal phase space is shown in figure 2.1.25a.

At the time of beam transfer the Recycler RF system is generating a pair ofconstraining barrier voltage pulses. In addition, between these pulses 4 wavelengths of2.5 MHz with a matching voltage of 1.6 kV (matched to the 3 eV-sec bucket in the MainInjector) provides bucket-to-bucket RF transfer. After adiabatically turning the 2.5 MHzsinusoidal waveform to zero, the transferred charge is cogged azimuthally to its storageposition (see figure 2.1.13b) and compressed. Figures 2.1.26 and 2.1.27 show the resultsof a ESME-like simulation of this operation, where the entire process takesapproximately 1 second with no measurable longitudinal emittance growth..

The second antiproton batch transfer occurs similarly (see figure 2.1.25c). When thebatch is moved to the left, it is merged with the first recycled batch. As shown in figure2.1.25d and 2.1.25e, this merger is accomplished by adiabatically reducing the voltage ofthe inner voltage pulses to zero. At this point the distribution of recycled antiprotons canbe compressed by moving the right barrier pulse to the left. This process was alsosimulated with an ESME-like computer program. The results are shown in figures 2.1.28and 2.1.29. Reducing the middle pair of voltage pulses separating the 12 eV-secdistributions in 2 seconds with an emittance growth of less than 5%.

Figure 2.1.28: Initial distribution in which two 12 eV-sec distributions areconstrained by a pair of 250 nsec long barrier RF pulse sets (not shown).


Figure 2.1.29: Final distribution in which the two 12 eV-sec distributionsare merged by linearly reducing the voltage of the intermediate barrierpulses in 2 seconds. Less than 5% emittance growth is observed in thesimulation.

This process of beam transfer continues until the last of 9 batches are injected. Figure2.1.30a shows the compression of the previous 8 batches necessary to leave sufficientazimuthal aperture to fire the injection kicker. Note that a voltage of 2 kV and a pulselength of 1 µsec is now necessary to constrain the recycled beam. After merging the 9thbatch (see figure 2.1.30b), the recycled beam is compressed into a pulse length ofapproximately 4 µsec, leaving sufficient room for the inverse operation of extracting thecooled antiprotons for injection into the next Tevatron Collider store (see figure 2.1.30c).

In a given allowed azimuthal time interval, the maximum bucket area is producedwhen the pair of barrier pulses have a total length equal to that interval. See figure 2.1.31for a sketch of this situation. The equation for this bucket area A is

A = 83 ∆E1/2 T . (2.1.13)

Table 2.1.9 contains parameters assuming storage of all of the recycled beam in 3.5 µsecassuming no emittance growth in any of the phase space manipulations above. Byincreasing the pulse width to 2 µsec each, equation (2.1.13) suggests that the bucket areawould increase by a factor of 30%, enough to encompass a healthy emittance growthcontingency.

It is anticipated that the minimum time between successive transfers of batches to theRecycler ring is approximately 20 sec. Therefore, the entire Main Injector decelerationcycle should be less than this time interval to keep the injection time as low as possible.Figure 2.1.32 contains a sketch of the timing of the Main Injector deceleration cycle.


(a)

(b)

(c)

(d)

Figure 2.1.30: End of the process of antiproton recycling from the MainInjector. The leftmost charge distribution is always the cooledantiprotons. In (d) the cooled antiprotons have been injected into theTevatron Collider and the recycled antiprotons have been debunched.

Barrier Voltage ε

τ

∆E1/2

T

Figure 2.1.31: Sketch of the phase space configuration of the maximumbucket area generated in a given azimuthal time interval (=2T).


Table 2.1.9: Recycler and RF parameters which produce the maximumbucket area with a limited voltage inside a prescribed fraction of thecircumference. The necessary RF bucket area is equal to the totalinvariant 95% longitudinal emittance of all the recycled antiprotons, whichis equal to 36 x 3 eV-sec = 108 eV-sec.

Parameter 36 BunchesInvariant 95% Longitudinal Emittance (eV-sec) 108Beam Total Energy (GeV) 8.938Relativistic Velocity 0.9945RF Voltage (kV) 2RF Pulse Length (µsec) 1.75Momentum Compaction Factor -0.008683RF Bucket Length (µsec) 3.5RF Bucket Half Height (MeV) 24RF Bucket Area (eV-sec) 112RMS Momentum Spread of the Beam (MeV) 12

Mai

n In

ject

or K

inet

ic E

nerg

y (G

eV)

0

30

60

90

120

150

0 10 20 30Time (sec)

Transfer from the Tevatron to the Main Injector of 4 antiproton bunches

Bunch rotation and capture in 2.5 MHz RF buckets

Transfer tothe Recycler

Deceleration through transition with the2.5 MHz RF system

Figure 2.1.32: Sketch of the Main Injector deceleration cycle in which 4recycled antiproton bunches are injected into the Recycler.

When all of the cooled antiprotons have been extracted, the recycled antiprotons canbe adiabatically expanded to fill the ring. As shown in figure 2.1.30d, by slowly reducingthe barrier pulse voltage to zero, the minimum momentum spread can be achieved.


Except for the portion of the azimuth carrying the overly compressed recycled antiprotonsduring extraction, the stochastic cooling is always turned on. In the above examplecalculations, assuming 3 eV-sec per recycled antiproton bunch and a healthy contingencyof emittance growth through all of the RF manipulations, a maximum rms energy spreadof approximately 3 MeV is expected.

2.1.7. Stacking from the Accumulator

In the Accumulator, a longitudinal emittance of 6.4 eV-sec is produced by thelongitudinal stochastic cooling system at low stack intensities. This corresponds to anrms energy spread of 1 MeV. As the stack intensity increases, both the longitudinalemittance and rms energy spread increase linearly. Therefore, if short bunches aredesired in the Tevatron Collider the Recycler ring acts as a necessary storage stage afterthe Accumulator.

It is anticipated that the optimum rate at which antiprotons are transferred from theAccumulator to the Recycler ring will be determined by a number of factors. First, as thestack size in the Accumulator increases the stacking rate eventually starts to decrease.Second, there will be considerable setup time preparing the transfer lines. This is becausethe 120 GeV proton transfer line to the antiproton target as an 8 GeV antiprotonextraction line must be used. Changing the energy of the line and tuning up the steeringbetween the Accumulator and the Main Injector could require up to 5 minutes for eachtransfer (in the mean time the Main Injector is not stacking, but still servicing other needssuch as 120 GeV fixed target or NuMI beam delivery). Third, if the momentum spread ofthe Accumulator is large compared to the Recycler stack and/or the momentumacceptance of the stochastic cooling system, time will be required to cool the beam beforethe next transfer. At present the best estimate for the optimum transfer rate is once every2 hours.

The actual transfer between the Accumulator and the Recycler should be quitestraightforward. Once a gap of sufficient azimuth is opened in the Recycler beamdistribution, the Accumulator beam can be injected via the Main Injector. According todata gathered from Accumulator operations, a 20x1010 antiproton/hour stacking rate anda 2 hour time between transfers generates an antiproton distribution each transfer with apulse length of 1.5 µsec, an intensity of 40x1010 antiprotons, a transverse emittance ofapproximately 10 π mmmr, and a momentum spread of 1.6 MeV. This corresponds to alongitudinal emittance of 10 eV-sec.

Therefore, the overall intensity history of the Recycler should look like the sketch infigure 2.1.33. The peak current in the ring occurs after the recycled antiprotons areinjected but before the cooled antiprotons are extracted. Since the transverse diffusionmechanisms are quite small and the Accumulator beam is already injected at the targetinvariant 95% transverse emittance of 10 π mmmr, transverse cooling times on the orderof a few hours are sufficient. In order to understand the demands on the momentumcooling system, an integrated model of the entire time evolution of antiprotondistributions shown in figure 2.1.33 must be synthesized.


Rec

ycle

r A

ntip

roto

n In

tens

ity (

E10

)

0

100

200

300

400

500

0 2 4 6 8Time (hours)

1 2 3Accumulator-to-Recycler Transfers

Antiproton Recycling

Injection into the Tevatron Collider

TevatronInjection

Figure 2.1.33: Anticipated time evolution of the intensity in the Recyclerring.

2.1.8. Antiproton Injection into the Tevatron Collider

In figure 2.1.30c the cooled antiprotons (left) and recycled antiprotons (right) arestored in the Recycler. At this point it is necessary to extract the cooled antiprotons. Theempty space occupied in figure 2.1.30c by the extraction kicker waveform is the locationwhere pulses of antiprotons are extracted into the Main Injector for injection into theTevatron Collider.

A total of 36 collider bunches must be extracted in 9 batches of 4 bunches. Therefore,the 1/9th of the cooled distribution is extracted at a time. The extraction process for eachbatch starts with the formation of a pair of barrier pulses formed adiabatically inside ofthe cooled beam distribution. By placing the pulses at the correct azimuth, the correctfraction of antiprotons are segmented into a separate distribution. This separatedistribution is then accelerated into the extraction azimuth.

Before the extraction kicker fires, the opposite adiabatic operation to that shown infigures 2.1.26 and 2.1.27 is implemented. The RF and beam parameters at this stage aresummarized in table 2.1.10. In this way 4 bunches spaced into separate 2.5 MHz RFbuckets are formed in the Recycler. When the extraction kicker is fired the Recycler andMain Injector 2.5 MHz waveforms are synchronized in amplitude and phase in order toavoid longitudinal emittance growth.

Once the transfer of 4 antiproton bunches into the Main Injector is accomplished, the2.5 MHz RF system in the Main Injector then accelerates the beam through transition to


25 GeV. At 25 GeV the antiproton distribution is bunch rotated, similar to the operationperformed on protons just before they are sent into the antiproton target. The purpose ofthis operation is to shorten the antiproton bunches sufficiently to allow capture into53 MHz RF buckets. Once the RF handoff is complete, the beam is accelerated the restof the way to 150 GeV and transferred into the Tevatron Collider. This entire process issummarized in figure 2.1.34.

Table 2.1.10: Recycler and RF parameters which produce the 2.5 MHzbucket just before injection of cooled antiprotons into the Main Injector.

Parameter per BunchInvariant 95% Longitudinal Emittance (eV-sec) 1.5Beam Total Energy (GeV) 8.938Relativistic Velocity 0.9945RF Voltage (kV) 2RF Frequency (MHz) 2.5Momentum Compaction Factor -0.008683RMS Bunch Length (µsec) .038RF Bucket Half Height (MeV) 6.9RF Bucket Area (eV-sec) 3.5Ratio of Bunch Area to Bucket Area 0.43

Mai

n In

ject

or K

inet

ic E

nerg

y (G

eV)

0

30

60

90

120

150

0 10 20 30Time (sec)

Transfer to the Tevatronfrom the Main Injector

Bunch Rotationand Capture in53 MHzRF Buckets

Transfer to the Main Injector

Acceleration through Transition with the

2.5 MHz RF System

RR: Unstack4 x 1.5 eV-secof Antiprotons

RR: Form Charge into 4 Bunches in 2.5 MHz Buckets

Figure 2.1.34: Sketch of the Recycler and Main Injector functions duringeach antiproton batch creation/extraction cycle.


2.1.9. Beam Cooling Requirements

In the above discussion the concept of stochastic cooling has been invoked but notexplained. The requirements for beam cooling in the above Recycler operational scenario(where luminosity leveling is not invoked) are summarized below.

1. Produce a stacked beam of 2.6×1012 antiprotons in a longitudinalemittance of 54 eV-sec and a normalized transverse emittance of10 π mmmr in an 8 hour cooling cycle (see table 2.1.2).

2. Accept recycled antiproton beams from the Tevatron at a nominalintensity of 1.5×1012 antiprotons, a maximum longitudinalemittance of 108 eV-sec and a maximum normalized transverseemittance of 30 π mmmr. This beam is the basis for forming thestacked beam for the next cooling cycle.

3. Accept beam from the Accumulator and add it to the stack at the rateof 0.2×1012 antiprotons per hour. The Accumulator beam has alongitudinal emittance of 10 eV-sec and a normalized transverseemittance of 10 π mmmr.

The design of the cooling systems to accomplish these functions is described in moredetail in section 2.9.

2.1.10. Nominal Cooling/Recycling Cycle

In order to better understand the following discussion, refer to figure 2.1.33. Thesimulation begins at 0:00 (hours:minutes) with a beam of 1.5×1012 antiprotons that hasbeen recycled from the Tevatron and is contained in a longitudinal emittance of108 eV-sec. A remnant of the cold antiproton beam which was in the tails of themomentum distribution and not transferred to the Tevatron collider contains 0.3×1012

antiprotons in 85 eV-sec. The recycled and remnant antiprotons have been previouslymerged and are contained between a pair of 2 kV barrier bucket pulses 1 µsec wide andseparated by 5.5 µsec. The recycled beam has a maximum normalized 95% transverseemittance of 30 π mmmr.

During the stacking cycle the barrier bucket holding the recycled beam is compressedto 2.3 µsec and beam is added from the Accumulator. Transfers from the Accumulatoroccur at 2:00, 4:20, and 6:40 in the stacking cycle. Each transfer contains 4.66×1012

antiprotons in 10 eV-sec longitudinally and 10 π mmmr transversely.At 7:20 a new batch of recycled antiprotons are injected and stored in a separate

barrier bucket in the Recycler. These antiprotons can be cooling, but for simplicity thesimulation assumes that the recycled beam is neither cooled nor heated until thebeginning of the next cycle. The cooling of the stacked beam continues until 7:40, whenthe outer (unusable) 85 eV-sec of the cooled antiproton momentum distribution arecombined with the recycled beam and the central 54 eV-sec are transferred to the


Tevatron. At this point the stacked beam has a normalized 95% transverse emittance of10 π mmmr. At 8:00, the cooling cycle repeats.

A technical description of the cooling system is given in section 2.9.

2.1.11. Effect of Failures

The average luminosity is calculated using equation (2.1.11) and the parameter valuesfor the store duration, fill time, and integrated luminosity per store. In tables such as2.1.1 there is typically a row which contains the predicted integrated luminosity per weekor month. This number is usually the integrated luminosity assuming the store is alwaysat the peak luminosity the entire time period, and then derated by a factor of 3. This iscommonly referred to as the Snowmass criterion. Given the average luminosity, a certainnumber of store hours in a week are thus required in order to achieve the Snowmasscriterion. It turns out that the recently completed Run I had a ratio of peak to integratedluminosity which was consistent with the Snowmass criterion. In the case of Run II withthe Recycler ring the same number of store hours per week will insure that theaccumulation rate of integrated luminosity predicted in table 2.1.1 will be achieved.

During Run II the dominant anticipated type of failure is unintended antiproton loss inthe Tevatron (i.e. the store ends unintentionally). During Run I Tevatron stores endedunintentionally at an average rate of twice per week. The worst time for such a failure isjust after injection, when the antiproton stack size is at its minimum. In the scenario withthe Recycler, during the couple of hours in which the cause of the store loss isinvestigated and the Tevatron is returned to an operational state, the recycled antiprotonshave been recooled and are ready for immediate injection into the Collider. Therefore, astore at approximately half of the nominal luminosity can occur almost immediately.

Using the same simulations as those shown above, this store would have an initialluminosity of 1.1x1032 cm-2 sec-1 and after 12 hours would have accumulated 2.8 pb-1 ofintegrated luminosity, almost identical to the MI case where a full store was underway.During this time the stack size has grown to 204x1010 antiprotons assuming a stackingrate of 17x1010/hr. The number of antiprotons recycled at this point is 72x1010, and theinitial luminosity of the next store is only 25% below Recycler scenario nominal.Assuming a normal store duration for that store, the subsequent store will have an initialluminosity which is 99% of nominal. In the absence of the Recycler, where theAccumulator is emptied to 40% of peak current each transfer, that same 12 hour periodwould yield no integrated luminosity. Therefore, the Recycler adds a level of versatilitywhich makes the Tevatron Collider complex much more tolerant of unintentionalTevatron store losses.


2.2. Lattice Issues

The Recycler ring lattice mimics closely the Main Injector lattice with two 4.267 mlong 1.45 kG gradient magnets in each arc half cell. The ring was designed such that itreplicated the Main Injector cell length and hence followed the footprint of the MainInjector. The center of the Recycler ring vacuum chamber is placed over Main Injector ata distance of 7' from the floor. The Recycler has been designed to have exactly the sameradius as the Main Injector. Figures 2.2.1 and 2.2.2 show the beam's eye, plan, andelevation views of both the Recycler and Main Injector in a standard arc cell.

The only exception to the rule that the Recycler is placed over the Main Injector is atMI-60, the RF straight section. Because of the power tubes over the Main Injector RFcavities, the Recycler ring swings to the radial outside by 18" at that straight section.Figure 2.2.3 shows a tunnel cross-section of the geometry in the MI-60 region.

The other straight sections are identical to the Main Injector. In figures 2.2.4 and2.2.5 plan and elevation tunnel views of a straight section and the dispersion cells whichsurround them are displayed.

The Recycler lattice is virtually indistinguishable from the Main Injector lattice, evenwith the bypass at MI-60 included. It is a strong focusing FODO lattice made up ofeither two gradient magnets or two quadrupoles (in the dispersion free straight sections)above each Main Injector quadrupole. The horizontal and vertical tunes of the Recyclerare split by an integer to minimize transverse coupling effects. The lattice has beendesigned to have base tunes of Qx=25.425 and Qy=24.415 with a maximum horizontaldispersion of 2 m and a corrected chromaticity of -2 units in each plane. Figure 2.2.5shows the lattice functions for the entire ring.

The Recycler is made of three basic cell structures. The first are the arc cells whichhave a horizontal phase advance of 86.8° and a vertical phase advance of 79.3°. Thereare 54 arc cells, each consisting of four 4.267 m magnetic length (add 88.9 mm to eachend for a physical length of 4.445 m) permanent gradient magnets with a half-cell lengthof 17.288 m. The different horizontal and vertical phase advance require differentgradients between the focusing and defocusing arc cell gradient magnets. In addition,pole faces of the arc gradient magnets include a sextupole component to reduce thechromaticity to -2 in each plane.

The second cell type is that of the (dispersion free) straight section cells with the samehorizontal and vertical phase advance as the arc cells. There are three lengths of straightsections; four 3 half-cell, two 4 half-cell, and two 8 half-cell to make a total of 18 straightsection cells, each made up of four 0.5 m long permanent magnet quadrupoles. Theseparation of the two quadrupoles at each focusing (defocusing) location was tuned tomatch the lattice amplitude functions of the arc cells.

The third basic cell type is that of the dispersion suppresser cell. These form adispersion suppresser insert (2 cells) on either side of each straight section to make a totalof 32 dispersion suppresser cells. The half-cell length of this insert is 12.966 m such thatthe product of the bend angle and cell length is exactly half that the arc cells, thuscanceling the horizontal dispersion. There are actually two flavors of this insert becauseof the two different straight sections lengths (i.e. 3 or 4 half-cells in length). One matchesbetween the arc and straight section focusing cells while the other matches betweendefocusing locations. The dispersion suppresser insert is made up of eight (2/3)*4.267 m


long (2.845 m magnetic, 3.023 physical) permanent gradient magnets and produce 180°of phase advance in both planes.

Figure 2.2.1: Tunnel cross-section in a standard arc cell showing a MainInjector dipole near the floor and a Recycler gradient magnet above it andnear the ceiling.

Figure 2.2.2: Plan and elevation views of both the Recycler and MainInjector beamlines. Note that the top magnets (shaded magnets in the planview) are the Recycler gradient magnets.


Figure 2.2.3: Tunnel cross-section at the MI-60 straight sections showingthe Main Injector RF cavities with the Recycler ring quadrupoles aboveand to the radial outside.

Figure 2.2.4: Plan and elevation views of the Main Injector (open frames)and Recycler (shaded rectangles) magnet deployments in a standardstraight section.


Figure 2.2.5: Plan and elevation views of the Main Injector (open frames)and Recycler (shaded rectangles) magnet deployments in a dispersionsuppresser cell.

Figure 2.2.6: The Recycler lattice. Note that this lattice is virtuallyidentical to that of the Main Injector.


Figure 2.2.7 The Recycler lattice near MI-60. Note that 8 specialquadrupoles have been placed around the dispersion suppresser gradientmagnets in order to match Twiss and dispersion functions distorted by themagnet moves required to generate the 18" radial bypass of the MainInjector RF stations.

Given that there are 104 cells in the Recycler, the above cell descriptions would inferthat the horizontal and vertical betatron tunes are 25.36 and 23.86, respectively. Inactuality, the phase advance in the region of the MI-60 bypass is not the standard straightsection or dispersion suppresser. The reason is that the half-cell length of the dispersionsuppresser cells on either side of the RR-60 straight section were lengthened by 2 m andthe RR-60 straight section half-cell length was shortened by the same amount toaccomplish the 18" radial bypass of the MI RF stations. The shorter cell length in thestraight section reduced the lattice functions in this region creating a greater demand onthe dispersion suppresser insert to match between the arc and straight section latticefunctions and cancel the dispersion. Figure 2.2.7 shows the lattice functions in the regionof the MI-60 bypass. Note the extra 8 quadrupoles in the dispersion suppressers on eitherside of the straight section. These are used to aid in the match between the straightsection and standard arc cells.

A special feature of the RR-60 straight section is its use as a phase trombone forRecycler tune control. Instead of distributing remotely adjustable quadrupoles around thering, the RR-60 quadrupoles are segmented into 5 families. By adjusting these circuits, atune variation of up to ±0.5 is attainable, although only a fraction of that is actuallyrequired and will be implemented in the initial phase of Recycler operations. Theadjustments in these circuits are coordinated in such a way that the Twiss parameters atthe ends of the straight section are unchanged. For the full tuning range from the basetune, the peak beta function inside the straight section can grow by about a factor of 3.


Therefore, the vacuum chamber will be round and have a 3" diameter in this region inorder to preserve the Recycler aperture.

Figure 2.2.8: A standard Recycler long straight section.

Figure 2.2.9: A standard Recycler short straight section.


Figure 2.2.10: Lattice functions for the Recycler MI-30 straight section.

Figure 2.2.11: Lattice functions for the Recycler MI-30 straight section,with the future high-beta insertion for electron cooling superimposed.


With the exception of MI-30, the other long and short straight sections are quiteunremarkable and similar to the Main Injector lattice. Figures 2.2.8 and 2.2.9 documenttheir lattice configurations.

At MI-30 the intention at Recycler commissioning is to have the lattice shown infigure 2.2.10, which is basically identical to the Main Injector lattice. In the future,electron cooling is necessary to meet the more aggressive luminosity goals envisioned forthe Tevatron Collider. Electron cooling requires a very long high-beta insertion in orderto effectively transfer transverse emittance from the antiprotons to the electron beam. Infigure 2.2.11 a β=200 m straight region approximately 80 m in length is superimposedover the commissioning lattice functions. In order to maintain the aperture of theRecycler ring with this high-beta insert, the round vacuum chamber at MI-30 will have tobe 6" in diameter.


2.3. Performance Projections and Modeling

A series of calculations and simulations have been completed to assess theperformance of the Recycler Ring. The Recycler is designed to accept antiprotons fromthe Accumulator and from the Main Injector at 8.9 GeV/c. The antiproton beam isrequired to be stored in the Recycler for many hours under the influence of a stochasticcooling systems with cooling times of approximately 2 hours. The long cooling timeprecludes the possibility of a complete tracking simulation of the entire accumulationscenario. Instead we rely on a combination of semi-analytic calculations and tracking ofparticles over a range of 105 to 106 turns (1-10 seconds of real time). In general thestrategy is to use the calculations to suggest criteria for alignment and field qualityrequirements and then utilize tracking simulations to observe the survivability of particlesin the model Recycler as a function of betatron oscillation amplitude and momentumoffset.

Tracking calculations are performed using the thin element tracking programTEAPOT [L. Schachinger and R. Talman, Particle Accelerators 22, 1987]. Because ofour inability to track particles for more than a few seconds we require survivability forparticles with oscillation amplitudes corresponding to at least 70 π mmmr (normalized)over the full ±0.3% momentum aperture of the Recycler. This oscillation amplitudecorresponds to the vertical physical vacuum chamber aperture and provides a 50% marginrelative to the specified 40 π mmmr dynamic aperture. As Recycler prototype magnetsbecome available it is assumed that these tracking calculations will continue utilizingmeasured field characteristics.

In this section we describe the sensitivity of the Recycler lattice (RRV10) to a varietyof alignment and field non-uniformities that manifest themselves as closed orbit errors,betatron function errors, horizontal-vertical coupling, and finite dynamic aperture. Thedescription of the Recycler lattice includes higher magnetic multipoles in combinedfunction and quadrupole magnets, and both magnet and beam position monitor alignmenterrors. As described in section 2.2 this lattice is based on a ~90° phase advance cell, witha maximum beta function of 55 m and a maximum dispersion of about 2 m. The verticaldispersion in the Recycler is essentially zero and the nominal tune is (Qx,Qy)=(25.425,24.415). The lattice functions for the Recycler ring are shown in figure 2.2.6.

2.3.1 Recycler error matrix and expected alignment tolerances

The Recycler Ring utilizes a total of 344 combined function (a.k.a. gradient) and 86quadrupole magnets to provide bending and optical focusing. Construction of the ringwith the expected optical characteristics depends upon the production and alignment ofmagnets with a high degree of accuracy. In addition, since these elements are allimplemented as permanent magnets, the absolute strengths need to be well controlled.

In the presence of alignment and magnetic field errors the Recycler lattice will exhibita number of effects including closed orbit distortion, variations from the nominal tune,beta function distortions, horizontal-vertical tune splits due to coupling, and limiteddynamic aperture. Magnetic field errors will be of two generic types; systematic andrandom. Systematic errors are reflected in a variation of the average value for a type ofmagnet relative to a desired value, while random errors refer to the width of the


distribution around the mean. The effects of systematic and random errors are differentand so we treat them separately here.

Two primary magnet classes are considered. The first class is represented by the long(4.3 m) and the short (2.8 m) gradient magnets, while the second class is represented bythe total of all quadrupole magnets. The short gradient magnets differ from the long intotal integrated bending strength, nominally 2/3 of the long magnets, in their gradient-to-dipole ratio, and in the absence of a built-in sextupole component. The quadrupolemagnets come in 10 flavors representing a variety of strengths. Magnet strengthrequirements are summarized in section 3.1.

Orbit, tune, beta function, and coupling sensitivities of the Recycler lattice have beencalculated for systematic and random magnetic and alignment errors for each class ofmagnet. Results are displayed in table 2.3.1 for systematic errors and in table 2.3.2 forrandom errors. Systematic sensitivities are calculated via direct application to theRecycler design lattice while random sensitivities are calculated via statistical expressionsas given below. Examples of specific orbit and lattice variations can be found in sections2.3.2 and 2.3.3.

Table 2.3.1: Sensitivity of the Recycler lattice to systematic errors. Root-mean-square orbit and beta function distortions, as well as tune shifts andglobal coupling strength are given for the indicated systematic errors. Alleffects are linear in the assumed underlying errors.

Orbit(σx)

∆Qx ∆Qy ∆βx/βx(rms)

∆βy/βy(rms)

∆Qmin

Gradient magnetsintegrated dipole strength ∆BL/BL=.0001*

0.3mm

integrated gradient ∆B'L/BL=.0001/inch

.037 -.037 38x10-4 98x10-4

skew quadrupole ∆B'sL/BL=.0001/inch

.0218

Quadrupole magnetsintegrated strength ∆B'L/B'L=.0001

.0004 -.0004 2.9x10-4 5.1x10-4

* Orbit entry represents a systematic shift between the short magnet and the target of 2/3the long magnet strength.

In table 2.3.1 it is assumed that the energy at which antiprotons are delivered to theRecycler will be adjusted to correspond to the average bending field in the long gradientmagnets. Thus the only entry for a closed orbit error is associated with a mismatchbetween the strength of the short magnet and 2/3 the strength of the long magnet. Asseen from the table a 10-4 systematic mismatch of these two magnets results in a 0.3 mmrms orbit distortion. The beta function distortion caused by gradient errors showsrelatively suppressed sensitivity in the gradient magnets. This is because of the natural


suppression to systematic gradient errors provided by the ~90° cells making up theRecycler. The sensitivity of the tune split to a systematic skew quadrupole has beenreduced by providing a one unit tune split between the horizontal and vertical tunes. Itshould be noted that table 2.3.1 makes no provision for any sort of systematic magnetmisalignment.

Table 2.3.2 shows the sensitivity of the lattice to both random magnetic andalignment errors. Closed orbit errors are evaluated utilizing the expression:

σx2(s)

βx(s)= 1

8sin2(πνx )βxi

i∑ (σθi )2 , (2.3.1)

where σθi is the rms bending angle error through the ith element. For a dipole magnetσθi is σBL/(Bρ) (horizontally) or σφ×BL/(Bρ) where φ is the roll angle (vertically). Forany magnet containing a field gradient, σθi is σd×B'L/(Bρ) where d is the transversedisplacement. The interpretation of the numbers in table 2.3.2 is that at any given pointin the ring, there would be a ~2/3 chance of observing an orbit distortion of<(σx/√β)×√β(s) if magnetic elements were fabricated and aligned to the noted tolerances.A total rms orbit distortion at any point due to a different set of errors can be calculatedby noting that distortions are linear in the corresponding errors and that all distortions addin quadrature. For example, a magnet-to-magnet (rms) strength variation of 5x10-4,accompanied by an rms displacement error of 0.25 mm and an rms roll angle of 0.5 mradwould produce an rms orbit distortion of 5.8 mm horizontally and 6.1 mm vertically(βav=33 m).

Beta function distortions are calculated using the expression:

σ ∆ββ

2 = 1

8sin2(2πν)(σkl )i

2

i∑ βi

2 , (2.3.2)

where σkl is the integrated gradient error, or the transverse displacement times theintegrated sextupole strength in the case of the long gradient magnets. The minimumtune split is calculated as

(∆νmin )2 = 1

2π2 (σksl )i2

i∑ βxiβyi , (2.3.3)

where σksl is taken as σφ times the nominal integrated gradient. For any set of errors theexpected rms beta distortion or minimum tune split can be calculated by scaling thenumbers listed in the tables and then adding in quadrature. For example, an rmsintegrated gradient error of 1×10-4/inch as referenced to the dipole field, accompanied byan rms 0.25 mm transverse offset would produce a distortion of 3.8% in both thehorizontal and vertical beta functions. It should be noted through a comparison of table2.3.2 with 2.3.1 that systematic (normal) gradient errors are more benign than randomerrors.


Table 2.3.2: Sensitivity of the Recycler lattice to random errors. Root-mean-square orbit and beta function distortions, as well as global couplingstrength are given for the indicated random errors. All effects are linear inthe assumed underlying errors and results add in quadrature

OrbitError

(σx/√βx)

OrbitError

(σy/√βy)∆βx/βx(rms)

∆βy/βy(rms)

∆Qmin

Gradient magnetsintegrated dipole strength σBL/BL=.0001

1.1x10-4

integrated gradient σB'L/BL=.0001/inch

386x10-4 375x10-4

skew quadrupole σB'sL/BL=.0001/inch

.0110

transverse displacement σd=.00025 m

7.9x10-4 8.4x10-4 54x10-4 84x10-4

roll σφ=.0005

4.6x10-4 .0040

Quadrupole magnetsintegrated strength σB'L/B'L=.0001

10.x10-4 9.8x10-4

transverse displacement σd=.00025 m

2.7x10-4 2.9x10-4

roll σφ=.0005

.0015

2.3.2 Closed orbit calculation and correction procedure

The Recycler contains 416 beam position monitors (BPMs), one horizontal and onevertical in each half cell. The closed orbit as observed on the BPM system is calculatedfor a random collection of alignment and bending strength errors as described intable 2.3.3. Orbit errors in the horizontal plane are generated by random transversemisalignments of the combined function and quadrupole magnets, and magnet-to-magnetbending strength variations, while in the vertical plane roll alignment errors replacestrength variations as a contributor.

Table 2.3.3. Random misalignment errors used in Recycler orbit andtracking simulations.

Magnet Type σBL/BL σh (mm) σv (mm) σroll (mrad)Gradient Magnet .0005 0.25 0.25 0.50Quadrupoles - 0.25 0.25 0.50Beam Position Monitors - 0.25 0.25 -


Ten sets of Recycler closed orbits are generated using random distributions ofstrength and alignment errors with rms widths as given in table 2.3.3. Errors aregenerated in Gaussian distributions cut off at 3σ. The equality of the magnet-to-magnetand roll distribution widths implies that the vertical and horizontal orbits will be the samein a statistical sense. As a result only the horizontal orbit is studied here.

A histogram of the distribution of observed rms horizontal orbit distortions is given infigure 2.3.1. The figure shows that the most likely rms orbit distortion for tolerancesgiven above lies in the 4-8 mm range. As can be deduced from table 2.3.2, magnet-to-magnet strength variation, transverse alignment, and roll errors all contributeapproximately equally to the closed orbit distortion.

0

1

2

3

4

2 4 6 8 10

rms Orbit Disortion (mm)

Nu

mb

er

of

Oc

cu

rre

nc

es

Figure 2.3.1: Probability distribution of expected uncorrected rmshorizontal orbit distortion based on the alignment and strength errors givenin table 2.3.3. Ten different ensembles of errors are calculated and enteredinto this histogram.

It will be desirable to correct the orbit to a residual distortion of under 1 mm. Becauseof the static nature of the Recycler it is possible to consider doing this by displacing thecombined function magnets transversely in an appropriate manner. Several differentstrategies are possible for identifying a finite set of magnets that could and should bemoved to correct the orbit. In the approach studied here a specific algorithm is applied toselect a set of magnet moves that reduce the rms orbit distortion. This algorithm isbelieved to have originated in the CERN SPS and is implemented as follows:

1. For the closed orbit given, find the single magnetic element in the ring for which amove minimizes the rms orbit distortion. If an element has to be moved more than5 mm in order to minimize the distortion that element is removed fromconsideration.


2. Find the second element that paired with the element identified in 1, is mosteffective in minimizing the rms orbit distortion. Again reject any element thatrequires a move of more than 5 mm to minimize the orbit distortion.

3. Repeat up to 15 times, always identifying the element to add to the previouslydefined list as most effective at minimizing the rms orbit distortion.

The effectiveness of the algorithm is demonstrated in table 2.3.4 and in figure 2.3.2.The table lists the rms and peak orbit distortions observed both before and aftercorrections for each of the ten generated orbits. In addition the maximum transversemagnet move is listed. The table indicates that in all cases the rms distortion can bereduced to less than 1 mm, with a peak distortion under 2.6 mm, by utilizing 15 suitablychosen magnet moves. In all instances the maximum magnet move is less than 3.3 mm.Figure 2.3.2 shows the entire uncorrected and corrected orbit for seed 8, the seed with theworst uncorrected orbit.

Table 2.3.4: Uncorrected and corrected orbit distortions for ten differentrandomly generated closed orbits. The column label "∆max" lists themaximum magnitude of the 15 magnet moves required to effect thecorrection.

Uncorrected Corrected (15 moves)Seed σH (mm) Peak (mm) σH (mm) Peak (mm) ∆max (mm)

1 2.87 6.85 0.65 2.61 2.542 5.69 13.45 0.66 2.17 2.233 7.83 17.57 0.65 2.04 2.804 2.69 6.35 0.52 1.66 3.285 7.55 17.27 0.75 2.04 2.726 2.49 6.02 0.73 2.08 3.067 6.06 11.01 0.56 1.52 2.898 9.00 16.40 0.73 1.79 2.699 5.67 11.33 0.77 1.84 2.82

10 3.69 8.87 0.59 1.77 2.06

2.3.3 Optical function errors

As discussed in section 2.3.1, combined function and quadrupole magnetic strengthand alignment errors change the beta function around the Recycler from that of the ideallattice. Figure 2.3.3 shows an example of the beta function distortion for a randomdistribution of gradient errors of 1x10-4/inch (rms, relative to the nominal dipole field) inthe combined function magnets and 8x10-4 of the nominal gradient in the quadrupolemagnets. The rms beta function deviation is a few percent and is dominated by thecontribution from the long combined function magnets. The relatively large (15%)variation on the right hand side of figure 2.3.3 is caused by adjustments in the phasetrombone at MI-60 required to maintain the tune at its nominal values in the presence ofthe gradient errors modeled.


No special provision are currently planned for correcting beta function distortions.Magnet performance specifications will be tailored to keep uncorrected distortions lessthan 2%.

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

0 500 1000 1500 2000 2500 3000 3500

s (meters)

XC

O

(mm

)

Uncorrected

Correction 15

Figure 2.3.2: The uncorrected and corrected orbit corresponding to seed 8in table 2.3.4. The corrected orbit is produced by transverse moves offifteen magnets around the Recycler.

-15

-10

-5

0

5

10

15

∆β/

β (%)

3.02.52.01.51.00.50.0

Path Length (Km)

Beta_x Beta_y

Figure 2.3.3: Typical beta function variation resulting from expectedgradient strength errors.


2.3.4 Field Non-uniformities

Magnet field non-uniformities can be characterized in terms of field multipoles. Thischaracterization is based on a description of the field in transverse coordinates via:

By + iBx = B0 (bn + ian )(x + iy)n

n=0

∞

∑ , (2.3.4)

where b0, b1, b2 . . . are the normal dipole, quadrupole, sextupole, . . . field components,and a0, a1, a2 . . . are the corresponding skew components. These higher-order fieldcomponents can produce tune variations with particle oscillation amplitude and canproduce unstable motion when the tune operating point comes close to fulfilling therelation

lνx + mνy = k , (2.3.5)

where l, m, and k are integers. The integers l and m are related to the field index nthrough the relation n=l+m-1.

The design tune of the Recycler is (Qx,Qy)=(25.425,24.415). This leaves itrelatively isolated from resonances up to fifth order. Tune variations with amplitude andone dimensional resonance widths up to tenth order have been calculated for oneFermilab "unit" of multipole component, where Fermilab units are defined as the ratio ofthe multipole strength to the dipole strength, measured at 1", times 10,000, i.e.

1unit = bnxnx=1"

×104 = B(n)xn

n!B0 x=1"

×104 . (2.3.6)

In quadrupole magnets the multipole strengths are referred to the quadrupole, rather thanthe dipole field. Resonance widths generated by higher order multipoles are much lesssignificant than tune variations with amplitude for the design tune point.

Sensitivity of the tune variation with amplitude to a given multipole contribution iscomputed using the expressions:

∆νn = ε(n−1)/2(n + 1)!

2n+2 π(n + 1

2)!2

bn,iθiβi(n+1)/2(39.37)n ×10−4

i∑ , (2.3.7)

∆νn = ε(n−2)/2n(n)!

2n+1π(n2

)!2∆pp

bn,iθiDxiβin/2(39.37)n ×10−4

i∑ . (2.3.8)

Here all lengths are measured in meters, θi is the bend angle in the magnet, Dx is thehorizontal dispersion function, and the particle oscillation amplitude is given by


x(s) = A β(s)cosφ(s) = εβ(s)cosφ(s). Equation 2.3.7 applies only to n=odd multipolesand equation 2.3.8 to even multipoles. Equation 2.3.8 represents the feed down effect inthe presence of non-zero dispersion and only leads to tune shifts for off-momentumparticles.

Table 2.3.5 displays the tune shift for a particle with a 6.3 π mmmr (60π/βγ)oscillation amplitude, accompanied by a momentum offset of 0.3%, generated by a zerothharmonic multipole contribution of one unit. This tune shift scales as A(n-1)/2 where Ais the amplitude and n is the field index in equation 2.3.4.

Table 2.3.5: Tune shift for a particle with an oscillation amplitudecorresponding to 60 π mmmr and a momentum offset of 0.3% arising fromone unit of the multipole component indicated in the left column. CF andQ refer to contributions from the combined function and quadrupolemagnets respectively.

Systematic Random (rms)n Multipole ∆ν(CF) ∆ν(Q) ∆ν(CF) ∆ν(Q)3 Octupole 0.0170 0.0003 0.0017 0.00004 10-pole 0.0122 0.0002 0.0012 0.00005 12-pole 0.0074 0.0001 0.0007 0.00006 14-pole 0.0079 0.0001 0.0008 0.00007 16-pole 0.0033 0.0001 0.0003 0.00008 18-pole 0.0048 0.0001 0.0005 0.00009 20-pole 0.0015 0.0000 0.0002 0.0000

2.3.5 Tracking calculations

The tune vs. amplitude analysis presented above provides a guide as to the allowedmultipole content of the magnets making up the Recycler. However, the Recycler isrequired to circulate beam for several hours and long term behavior in the presence of thefull collection of misalignment and field errors is best understood through trackingsimulations.

Performance in the presence of a mixture of alignment and magnetic field errors inthe Recycler is tested by launching an array of particles at different amplitudes in thepresence of the full array of errors described in sections 2.3.2-4. Particles are trackedwith betatron oscillation amplitudes relative to a corrected closed orbit. Followingintroduction of errors the tune is adjusted to the nominal tune for a zero momentum offsetparticle using the phase trombone. The criterion for acceptable performance is survivalover 105 turns (1 second of real time) with an oscillation amplitude corresponding to60 π mmmr over the full momentum range of ±0.3%. The emittance of the recycledbeam is expected to lie in the 20-25 π mmmr range, while 0.3% corresponds to themomentum acceptance of the stochastic cooling systems.

Specifically, particles are launched with a horizontal displacement "A" and a verticaldisplacement βy βx A , i.e. the particle has equal horizontal and vertical emittance. Intranslating into acceptance the displacement is referred to a horizontal beta function of65 m (xLaunch = βx 65 A ). Particle are tracked with a constant momentum offset of,


∆p/p, which is varied over the range ±0.3%. Net chromaticities in both planes are set to-2, the correct sign to combat the bunched-beam head-tail instability. Particles withamplitudes varying from 15 mm to 35 mm are considered. Simulations are performed forfive different seeds with a maximum of 100,000 turns tracked.

Combined function multipole component errors used in these simulations are given intable 2.3.6. As a starting point application of a criterion of detuning of less than 0.03 at60 π mmmr was applied to table 2.3.5 in the presence of a 0.3% momentum offset. Thesemultipoles were observed to result in a dynamic aperture somewhat less than the goal of60π. As a result the multipole composition was varied with the set presented belowleading to acceptable behavior. This set provides the basis of the current magnetspecification as described in section 2.3.6. Further iteration on this set is anticipated.Multipole component errors used for the quadrupole magnets are given in table 2.3.7.Performance is relatively insensitive to these multipoles (at the factor of three level).Note that all systematic multipoles are modeled with the same sign. This is the mostpessimistic assumption possible because it results in the maximum detuning withamplitude. It is worth noting that in the absence of any ≥8-pole errors the aperture of theRecycler is in excess of 100 π mmmr over the entire specified momentum range.

Table 2.3.6 Combined function magnet field multipoles used in thetracking simulations represented in figure 2.3.4. All multipoles are givenin Fermilab "units" as referenced to the dipole component.

MultipoleComponent

Normal(Systematic)

Normal(Random)

Skew(Systematic)

Skew(Random)

Quadrupole 1.0 1.0 1.0 1.0Sextupole 0.5 1.0 0 0.5Octupole 0.5 0.5 0 0.510-pole 0.2 0.5 0 0.512-pole 0.1 0.5 0 0.514-pole 0.1 0.5 0 0.516-pole 0.1 0.5 0 0.518-pole 0.1 0.5 0 0.520-pole 0.1 0.5 0 0.5

Table 2.3.7: Quadrupole magnet field multipoles used in the trackingsimulations represented in figure 2.3.4. All multipoles are given inFermilab "units" as referenced to the quadrupole component.

MultipoleComponent

Normal(Systematic)

Normal(Random)

Skew(Systematic)

Skew(Random)

Quadrupole 0 8 0 0Sextupole 0.5 0.5 0 0.5Octupole 0.2 0.5 0 0.510-pole 0.1 0.5 0 0.512-pole 0.1 0.5 0 0.514-pole 0.1 0.5 0 0.516-pole 0.1 0.5 0 0.518-pole 0.1 0.5 0 0.5


0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

1.00E+05

1.20E+05

30 29 28 27 26 25 24 23 22 21 20 19 18 17 16

Particle Amplitude at Beta Max of 65m (mm)

Tim

e B

efor

e L

oss

(In

Tur

ns)

Figure 2.3.4: Survival plot for the Recycler. The number of turnssurvived, up to 100,000 turns, is shown as a function of the launchamplitude for five different collections of systematic and randomalignment and magnetic field errors and a momentum offset of 0.3%.

0

10

20

30

40

50

60

70

80

90

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

∆P/P (%)

Dyn

amic

Ape

rtur

e (π

mm

mr)

Figure 2.3.5: Dynamic aperture as a function of momentum offset over thefull momentum range of the antiproton stack. This calculation is based on100,000 turn survival and incorporates the full set of misalignment andfield quality errors described in the text.


Figure 2.3.4 is a survival plot displaying how many turns a particle survives in theRecycler as a function of initial amplitude for each of five seeds. If the dynamic apertureof the machine is defined as the smallest amplitude particle that did not survive for100,000 turns, then the dynamic aperture for the Recycler is predicted to be 22±1 mm,corresponding to a normalized emittance of 64±6 π mmmr.

Figure 2.3.5 shows the dynamic aperture as determined by 100,000 turn particlesurvival as a function of the momentum offset. This plot indicates that an aperture inexcess of 60 π mmmr is maintained over the full momentum spread expected in theantiproton stack. Further tracking of up to 106 turns is currently being undertaken tounderstand longer term trends.

Particle tracking is also utilized to study the variation of the horizontal and verticaltunes as a function of oscillation amplitude. Figure 2.3.6 shows the tune space locationas a function of amplitude for particles with a 0.3% momentum offset. Comparison withtable 2.3.5 shows that the vertical tune shift with amplitude is nearly completelyaccounted for by the 0.5 unit systematic octupole component assumed in the tracking,while the other multipoles conspire to keep the horizontal tune shift small.

Tune vs. Amplitude

0.406

0.408

0.41

0.412

0.414

0.416

0.418

0.42

0.422

0.424

0.426

0 5 10 15 20

Amplitude (mm)

Tune

QxQy

Figure: 2.3.6: Tune vs. amplitude for the set of multipoles given in Table2.3.6 as determined through tracking.

2.3.6 Magnetic performance specification

Magnet performance specifications have been developed based on the analysesdescribed in the above sections. The detailed performance specification is given inMI-0170 and is summarized here.

Tolerances have been specified for both systematic and random strength variations inthe dipole, quadrupole, and sextupole field components, overall magnetic field uniformityacross the required aperture, and allowed multipole composition. Criterion applied inderiving these tolerances are as follows:


1. Uncorrected closed orbit distortion due to magnetic field imperfections < 3 mm.

2. Beta function error due to magnetic field imperfections < 2%.

3. Tune relative to the nominal value within 0.1

4. Uncompensated minimum tune separation due to magnetic imperfections < .005

5. Tune variation with amplitude <.01 out to 20 mm.

6. Chromaticity within range of the sextupole correction system.

7. Beam survival at 20 mm oscillation amplitude for 5 seeds at 105 turns over thefull ±0.3% range of momentum offsets.

Tolerances are summarized in tables 2.3.8 and 2.3.9 below.

Table 2.3.8: Magnet strength tolerances for Recycler combined functionmagnets.

Performance Measure Tolerance(Systematic)

Tolerance(Random, rms)

Absolute bending strength of longcombined function magnet

5x10-4 5x10-4

Ratio of short/long bending strength incombined function magnets

5x10-4 5x10-4

Ratio of gradient to nominal dipole incombined function magnets

2x10-4/inch 1x10-4/inch

Ratio of sextupole/dipole in long combinedfunction magnets

1x10-4/inch2 1x10-4/inch2

Field flatness over ±20 mm ±1.5x10-4 ±1.5x10-4

Table 2.3.9: Allowed multipole components, in Fermilab units, forcombined function magnets. For quadrupole and sextupole components,the number listed is relative to the nominal design value.

MultipoleComponent

Normal(Systematic)

Normal(Random)

Skew(Systematic)

Skew(Random)

Quadrupole 1 1 1 1Sextupole 0.5 1 - 0.5Octupole 0.5 0.5 - 0.510-pole 0.2 0.5 - 0.512-pole 0.1 0.5 - 0.514-pole 0.1 0.5 - 0.516-pole 0.1 0.5 - 0.518-pole 0.1 0.5 - 0.520-pole 0.1 0.5 - 0.5


2.3.7 Required correction systems

Correction strategies and/or systems will be required to compensate for the magneticfield imperfections and misalignment effects described above. Systems or strategies arerequired for closed orbit correction, tune and chromaticity adjustment, couplingcorrection, and higher order resonance correction.

It is proposed that the closed orbit be corrected through adjustment of the transversepositions of a limited number of gradient magnets as described in section 2.3.2. Noactive correction elements are included in the design other than in the injection andextraction areas. As discussed in section 2.3.2 the uncorrected closed orbit is expected toshow peak excursions of up to ~15 mm. A model in which fifteen gradient magnets arechosen to be moved was analyzed and shown to produce a corrected orbit distortion of <1mm (rms) with peak distortions under 3 mm. The maximum transverse movementrequired is typically 2 mm, well within the range of tolerable mechanical motion allowed.

Tune adjustment is provided in the MI-60 phase trombone as described in section 2.2.Five families of two adjustable magnets each are provided. A total tuning range of ±0.5is achievable with no perturbation of the optical functions outside the trombone region.

A chromaticity control (sextupole) magnet system will be incorporated into theRecycler. The incorporation of a design systematic sextupole component into the longcombined function magnets will produce an uncorrected chromaticity in the Recycler of-2 in both transverse planes. A correction system is specified that allows adjustment ofthe chromaticity over a ±5 range relative to nominal in each plane. The total requiredstrength of focusing and defocusing sextupoles as a function of chromaticity is given intable 2.3.10. As is shown a total strength (B"L) of 425 kG/m is required. Such acorrection system will be implemented by utilizing unused Main Ring sextupoles. It isproposed to utilized two sets of sextupoles, 8 focusing and 16 defocusing, each to providechromaticity control in the Recycler. Each set will be constituted of several pairs ofmagnets separated by 180° of phase in order to nullify any contribution to the third orderresonant driving term.

Table 2.3.10: Sextupole strength required to achieve the Recyclerchromaticities listed in the left hand columns. B"L is the integratedstrength and NF,D is the number of magnets in each family. It is proposedto utilize a system in which NF=8 and ND=16.

∆ξH ∆ξV NF(B"L)F (kG/m) ND(B"L)D (kG/m)

+5 0 176 -690 +5 34 -355

+5 +5 211 -424

As described in section 2.3.1 coupling due to systematic and random skewquadrupole components, and due to alignment errors could be significant in the Recycler.Global coupling will be controlled via two skew quadrupole circuits. The location ofthese magnets depends on details of the lattice and will not be defined until the lattice isfrozen. All tracking simulations performed to date incorporate uncompensated coupling.


2.3.8 Summary

Calculations presented in this section have shown that the Recycler ring can achievethe design specification for storage of beam with a 40 π mmmr admittance and amomentum spread of 0.3%. This performance requires magnets built to tolerances listedin section 2.3.6, alignment at the level described in section 2.3.2, and correction of theclosed orbit. Magnet requirements are dictated by the allowable orbit and beta functiondistortions, and by the dynamic aperture in the presence of higher order magneticmultipoles.

It is anticipated that once full length prototype Recycler magnets have been measuredthe studies described here will be expanded more systematically to construct aperformance model of the real Recycler ring.


2.4. Beamlines and Beam Transfers

The desired functionality of the Recycler ring requires the addition of three 8 GeVproton and antiproton transfer lines. These transfer lines are shown on the right side offigure 2.4.1. The MI-32 and MI-40 proton injection and abort lines are used duringcommissioning and tune-up. The MI-22 and MI-32 antiproton transfer lines between theMain Injector and the Recycler are used for normal Tevatron Collider operations.

RR

MI-40 ProtonAbort

MI-40 ProtonAbort

MI-10 ProtonInjection

MI-52 ProtonExtraction

MI-62Antiproton Extraction

MI

MI-32 AntiprotonInjection

MI-22 AntiprotonExtraction

MI-22AntiprotonInjection

MI-32AntiprotonExtraction

Figure 2.4.1: Sketch of the Main Injector (MI) and Recycler ring (RR)beam transfer lines. Note that the transfer lines at the MI-22 and MI-32straight sections link the two rings together for injection and extraction ofboth antiprotons and protons.

2.4.1. Maximum Acceptable Kicker Ripple

The parameters which must be specified in order to design the kickers for thesetransfers are the kicker amplitude, rise/fall time, and flattop ripple magnitude. Theallowed magnitude of kicker flattop ripple is determined by the amount of emittancegrowth which is considered acceptable. The equation describing the fractional emittanceincrease due to a position or angular misalignment normalized to the beam rms size ordivergence respectively is

εεo

= 1 + 12

∆σ

2. (2.4.1)

According to equation (2.4.1) a given kicker amplitude error ∆ causes more emittancegrowth ε/εo as the initial beam divergence σ or emittance εo decreases. Usingconservative numbers for the initial emittance and the acceptable level of emittancegrowth, table 2.4.1 displays the relevant parameters which determine the percentagekicker amplitude ripple or error. The dependence of emittance growth on kicker error isplotted in figure 2.4.2.


Table 2.4.1: Anticipated parameters dictating the acceptable level ofkicker amplitude error or ripple during flattop.

Parameter ValueMaximum emittance growth (95% Invariant π mmmr) 0.2Minimum initial emittance (95% Invariant π mmmr) 10Maximum kicker error / beam divergence (equation 2.4.1) 0.2Beta function at the kicker magnet (m) 54Minimum beam divergence at a kicker magnet (µrad) 57Maximum deflection angle in a kicker (µrad) 12.0Kicker amplitude in all transfer lines (mrad) 1.0Maximum percentage kicker ripple/error magnitude (%) ±1.2

∆/σ

Em

ittan

ce G

row

th (

%)

0%

10%

20%

30%

40%

50%

0 0.2 0.4 0.6 0.8 1

Figure 2.4.2: Fractional emittance growth as a function of the transferangle or position error normalized to the rms beam divergence or size.

2.4.2. Role of Each Recycler Transfer Line

MI-32 Proton MI to RR: Used for commissioning and beam line tune-ups, the abilityto easily inject protons into the Recycler from the Main Injector is necessary for efficientstartup and operation. One positive aspect of the positioning of this transfer line is thefact that once the Main Injector is commissioned to its abort dump (which is the first halfturn of the ring), Recycler commissioning can also start.

MI-40 Proton Abort: Used only during commissioning or other proton applications inwhich high intensities of beam can cause radiation safety or ground water activationproblems, this abort line is basically identical to the Main Injector line. Since there is noemergency abort scenario envisioned, the kicker pulse length need only be 1.6 µsec inorder to fulfill its ALARA mission. In the unlikely situation of multiple proton batchinjection into the Recycler ring, multiple abort line transfers can be programmed to


eliminate this beam. Figure 2.4.4 shows the geometry of this abort line showing the ringquadrupoles, the horizontal kicker, and the vertical Lambertson magnet.

Q400 Q401 Q402

Horz.Kicker(1 mrad,1 m long,0.3 kG)

Vert.Lambertson(20 mrad,4 m long,1.5 kG)

Q403

Figure 2.4.4: Elevation view of the Recycler ring MI-40 proton abortextraction geometry. The horizontal kicker deflects the extracted beam by1 mrad into the bend field region of the vertical Lambertson magnet.

MI-22 Antiproton MI to RR: This transfer line directs antiprotons from the MainInjector and delivers them into a clockwise trajectory in the Recycler ring. Theantiprotons are either enroute from the Accumulator or have been recycled from theTevatron Collider. The maximum beam pulse length in either case is 1.6 µsec.

MI-32 Antiproton RR to MI: This transfer line directs cooled and formed antiprotonsfrom the Recycler ring and delivers them into the Main Injector ready for accelerationand transfer into the Tevatron Collider. The kicker flattop must be at least 1.6 µsec.

2.4.3. Kicker and Lambertson Placement

In the Main Injector, it is possible to use the same kicker at MI-30 for both transferlines at MI-32 and MI-22. By using a Recycler kicker at MI-20 for recycled antiprotoninjections at MI-22, the Recycler kicker at MI-22 away from any service buildings can beeliminated. This choice of kicker location is dictated by the fact that there is availablespace in that service building for the kicker hardware. Not only does the eliminate thecivil construction cost of building a dedicated kicker building, but it also symmetrizes thetwo transfer lines about MI-30. As required, the betatron phase advance between theMI-20 and the MI-22 Lambertson is an odd multiple of 90°. Similarly, the kicker atMI-32 can be eliminated by using the MI-40 abort kicker. Therefore, the number ofkickers is reduced from 6 to 3, a factor of 2 reduction. This scenario is sketched infigure 2.4.5. The advantages of this scheme are reduced cost and reduced Recycler ringimpedance.

The details of the positioning of the MI-30 kicker in the Main Injector and theassociated antiproton injection and extraction Lambertsons are sketched in figure 2.4.6.Since MI-22 and MI-32 are three half cell straight sections, the Main InjectorLambertsons are placed in those locations. In the Recycler there is so much free spacebetween the gradient magnets that Lambertsons easily fit even in bend cells. The onlycatch is the leading gradient magnets at 216 and 328 need to be half (mirror) magnets inorder for the extracted beam to clear with a 20 mrad kick.


K

L L

K

L

KL

L

Figure 2.4.5: Sketches of the Main Injector (left) and Recycler ring (right)transfer lines in which only the new Lambertsons and kickers needed forRecycler ring operations are depicted. The displayed scenario assumesthat kicker systems can be shared to service all of the transfer needs for afactor of 2 reduction in the number of systems.

305307309311313315317319 303 301231 229 227 225223 221 219217 215321323325327329

305307309311313315317319 303 301231 229 227 225223 221 219321323

Main Injector

K LL

L LRecycler

Figure 2.4.6: Sketch of the precise locations of the kickers andLambertsons for the antiproton injection and extraction lines at MI-22 andMI-32.

Lattice designs and beam envelope calculations of the MI-22 and MI-32 transfer lineshave been carried out [D. Johnson, MI Note 161]. The beam trajectories and full widthsfor the two machines and antiproton transfer directions are shown in figures 2.4.7 through2.4.10. In figure 2.4.7 the antiproton recycling transfer from the Main Injector to theRecycler via MI-22 is shown from the point of view of the Main Injector. The closedorbit between the kicker and Lambertson is distorted with a pair of correction dipoles inorder to optimize the use of horizontal aperture. The kicker launches the extracted beamon an opposite distortion which leads the beam into the Lambertson extraction channel.Both beams are assumed to have a transverse normalized 95% emittance of 40 π mmmr.The top and bottom of the plot are at the horizontal aperture of the Main Injector. Infigure 2.4.8 the recycled antiprotons are shown in the Recycler ring just downstream ofthe injection Lambertson. In this case the horizontal aperture of the Recycler is explicitlyindicated, and the beams are assumed to have an emittance of 20 π mmmr.


Figure 2.4.7: Beam trajectories and full widths of the stored and extractedbeam in the Main Injector during antiproton recycling transfers from theMain Injector to the Recycler. The Main Injector horizontal aperture is atthe extrema of the Y-axis of the plot.

Figure 2.4.8: Beam trajectories and full widths of the stored and injectedbeam in the Recycler during antiproton recycling transfers from the MainInjector to the Recycler.


Figure 2.4.9: Beam trajectories and full widths of the stored and extractedbeam in the Recycler during transfers of cooled antiprotons from theRecycler to the Main Injector.

Figure 2.4.10: Beam trajectories and full widths of the stored and injectedbeam in the Main Injector during transfers of cooled antiprotons from theRecycler to the Main Injector. The Main Injector horizontal aperture is atthe extrema of the Y-axis of the plot.


Extraction of cooled antiprotons from the Recycler for ultimate injection in theTevatron Collider takes place via the MI-32 transfer line. In figure 2.4.9 the closed orbitand extracted beam orbits are shown between the kicker and Lambertson. A transversenormalized 95% emittance of 10 π mmmr was used to calculate the full beam widths ofboth the circulating and extracted beams. The beam trajectory and size after the transferin the Main Injector is shown in figure 2.4.10.

2.4.4. Kicker and Lambertson Requirement Summary

In the transfer scenarios described in this design all kickers have an integrated kick of300 Gauss-meters. The maximum kicker length in all of these scenarios is approximately4 meters. In all cases the flattop duration of the kicker is at least 1.6 µsec. The rise andfall times for the two Recycler and one Main Injector kickers can be as large as 1-2 µsec.The minimum repetition interval for firing the kickers is anticipated to be 20 sec forantiproton transfers. Within the scope of Fermi III the proton injections are also limitedto this interval.

In order to minimize the impedance effects of the two kickers in the Recycler, thebeam tubes should be shielded or coated as much as possible. A reasonable criterionwould be for the coating to slow down the rise and fall times by approximately 5-10%.Because of the slow rise times in these kickers, a rather thick coating can be used.

The Lambertsons are of the permanent magnet variety. Since there is a verticalcorrection magnet next to each vertically bending Lambertson, the tolerance on the fieldstrength can be relaxed to as much as 1% (though in construction a manufacturingtolerance of 0.1% will be employed). The nominal bend angle of the Lambertsons is±22 mrad.

2.4.5. Beam Synchronous Clocks and Beam Transfers

From the very beginning of accelerator operations at Fermilab, the transfers of beamsfrom one accelerator to another has been complicated by the large number of transferlines and beam dumps. As the years have gone by, especially with the addition of theAntiproton Source, the complexity of beam transfers has increased dramatically. Withthe addition of the Main Injector and Recycler, this trend definitely continues.Figure 2.4.11 contains a diagram of all of the beam destination options.

Since the advent of the Tevatron accelerator in the early 1980's, beam transfersbetween accelerators have generally taken advantage of beam synchronous clocks.Presently realized for the Main Ring and Tevatron, beam synchronous clock basefrequencies are integer sub-harmonics of the machine RF (RF/7) while also synchronouswith machine revolution frequency, each having 159 clock ticks per revolution. Similarin operation to TCLK, events exactly synchronous with a machine's revolution frequency(RF/1113) are coded onto each of these clocks and are denoted by the hexadecimal codes$AAMRBS and $AATVBS. The existing capability to transfer beam from any particularRF bucket of one machine to any particular bucket of another machine will be retainedfor the planned Recycler. Conceptually expressed, desired transfers between machinesare allowed (or manipulated) to occur as the respective revolution events come intoparticular time (better stated as RF) alignment. Actual transfers are thereupon initiated byunique coded beam synchronous events that are placed constantly with respect to the


revolution events. Required kicker timing is provided by beam sync timer modules thatreference the unique transfer event and provide desired delay in machine revolutions andfractions thereof.

Tevatron

MainInjector

Booster

LinacNTF

400 MeV Dump66 MeV

400 MeV

400 MeV

8 GeVL13

Dump

Debuncher

Accumulator

AP0 Target

Recycler

MI-40Dump

NuMI

8 GeV

120 GeV150 GeV

150 GeV

1 TeV800 GeV

Switchyard

C0 Dump A0 Dump

Protons Antiprotons

Figure 2.4.11: Map of all of the beam destination options at Fermilab afterconstruction and commissioning of the Main Injector and the Recycler.

Transfers between the Recycler and Main Injector, which will require transfercogging of the Main Injector RF, are relatively uncomplicated since the 53 MHzharmonic numbers of each machine both equal 588. Booster or Accumulator transfers tothese larger machines are slightly more complicated in that their harmonic numbers are84. However, transfers are simplified by the fact that the Booster and Accumulatorharmonic numbers are exactly 1/7th that of the Recycler or Main Injector and that beamin either the Booster or Accumulator is, at least initially, uniformly distributed inlongitudinal space.

The Recycler will require a new RF system and a derivative beam synchronous clock,RRBS, to facilitate beam transfers and circulating beam diagnostics. For this clock,$AARRBS is the assigned revolution marker event and there are 84 clock ticks perrevolution. Development and installation of the new RRBS clock is judged as straight-forward in that RRBS architecture will largely duplicate that of other beam synchronous


clocks. RRBS will be distributed from MI-60 to all Main Injector service buildings andto the Booster via fiber optic links.

Careful coordination of the Booster, Recycler, Main Injector, and Accumulator RFsystems is fundamental to achieving successful transfers of beam. The fundamental53 MHz reference of the Recycler RF system is to be considered as a fixed reference at8 GeV to which other systems transfer cog and phase lock. While the operation of theAccumulator RF system has historically been independent, better synchronism strategieswith the Main Injector need to be developed. The Recycler RF system will routinelyprovide appropriate barrier buckets for acceptance of beam while also partitioningfractions of circulating beam for extraction.

2.4.6. Beam Synchronous Transfer Events

A variety of new beam sync transfer events have been designated to effect desiredtransfers of particle beams to and from the Recycler. These events are temporallydenoted by $SnxxBS, with n ranging up from one, and with the subscript denoting thespecific beam sync clock. Proper generation of these events ties closely with Recycleroperating scenarios previously described and the TCLK resource. Details relative to theassignment and generation of these events are described hereafter. Discussion isfacilitated by first describing the general sequence of TCLK and beam sync events on aper scenario basis. BES denotes the "Booster Extraction Sync" pulse signal presentlygenerated by the Booster low-level RF timing hardware. It is also worthwhile to note thatall beam sync transfer events are detected and mirrored as TCLK events with typicalrelated time skew of 100 nanoseconds or less. This mirroring of beam synchronoustransfer events in the Tevatron Clock has proven useful for diagnostic purposes.

S1: Main Injector Protons to the Recycler$T6 --> $2D --> $16 --> BES --> $S1MIBS --> $S3MIBS

S2: Recycler Protons to the Main Injector$T4 -->$S3RRBS --> $2F

S3: Accumulator P-Bars to the Recycler$T7 --> $9A --> $2D --> $7AMIBS --> $S4MIBS

S4: Recycler P-Bars to the Main Injector$T5 --> $2A --> $S4RRBS(Multiple sequences of $T5 Recycler cycles and $2A Main Injector cyclesare necessary to fill the Tevatron.)

S5: Tevatron P-Bars to the Recycler$CE --> $T8 --> $T9 --> $T7 --> $2A --> $T10 --> $25 --> $S2MIBS -->$T11 --> $T12 --> $T13 --> $S4MIBS(Multiple sequences of $T7 Recycler and $2A Main Injector cycles arenecessary to empty the Tevatron of p-bars once the Tevatron is at 150 GeV.)

$S1RRBS: Initiate Proton Transfer from Recycler to Main Injector - This transferevent will be generated in a typical fashion by having a TCLK timer channel output syncup with the first available decoded $AARRBS event to form the $S3RRBS event request.$T4 appears to be the natural reference. It could also process the output of a timerchannel with a $2D reference with a state machine to form the appropriate event request.


$S3RRBS: Initiate Antiproton Transfer from Recycler to Main Injector - This transferevent will be generated by having a TCLK timer output sync up with the first availabledecoded $AARRBS event to form the $S4RRBS event request. $T5 appears to be thenatural reference though it may be too far away in time. It could also process the outputof a timer channel with a $2A reference with a state machine to form the appropriateevent request.

$S1MIBS: Initiate Beam Transfer from Booster to Main Injector - Generation of thisevent would require some state machine processing of the BES pulse from the Booster.For the general case, the occurrence of any Main Injector reset and the occurrence of anyBooster reset except $17 would cause $S1MIBS to be generated. It is necessary to haveBES at MI-60, the location of the Main Injector RF system and the MIBS source, if the$S1MIBS event is to be accurate. State processing of the $1F event might also serve asthe event request for $S1MIBS. The possibility of timing the injection kicker at MI-10with BES, as alternative to $S1MIBS, remains as a viable option.

$S2MIBS: Initiate Antiproton Transfer from Tevatron to Main Injector - Transfercogging and diagnostic concerns again suggest this transfer event to be best placed on theMIBS rather than the TVBS clock. This event will be generated by having a TCLK timerchannel output sync up with the first available decoded $AAMIBS event to form the$S2MIBS event request. New event $T10, which occurs when the Tevatron ramp hasreached 150 GeV after the deceleration process, is likely the best reference for the timerchannel. Some state machine processing of the actual event request signal is likely.

$S3MIBS: Initiate Proton Transfer from Main Injector to Recycler - This transferevent will be generated by having a TCLK timer channel output sync up with the firstavailable decoded $AAMIBS event to form the $S3MIBS event request. $T6 appears to bethe natural reference. It could also condition the output of a timer channel with a $2Dreference with a state machine to form the appropriate event request.

$S4MIBS: Initiate Antiproton Transfer from Main Injector to Recycler - This transferevent is somewhat special in that two TCLK timer channels, one for each of the relatedS3 and S5 scenarios, are necessary to support event generation. The or'd timer channeloutputs will sync up with the first available decoded $AAMIBS event to form the$S4MIBS event request. For the S3 scenario, either $T7 or $9A appear to be the naturalreference for the first timer channel, the choice depending on their relative position intime. Some state machine processing is anticipated. For the S5 scenario, theaforementioned $T11 might serve as a reference for the second timer channel. One couldalso consider $T13 which occurs when the Main Injector ramp has reached 8 GeV afterthe deceleration process. As for the previous case, some state machine processing isprobably required.

2.5. Vacuum Issues

Stainless steel beam tubes in which the vacuum is maintained with lumped ion-sputterpumps is the traditional technology used in the hadron accelerators at Fermilab. Thoughan aluminum alternative is under serious consideration, this report will discuss a stainlesssteel system in which innovations are applied to bring down the cost without invokingunreasonable technical risks. An important factor affecting the design of the system is


the need for high reliability storage of the antiprotons. With the stated goal of survivinglightning strikes and power outages of up to an hour, manual sector valves and lowoutgassing rate beam tubes are required.

2.5.1. Beam Intensity Lifetime Requirement

The required beam intensity lifetime is determined by modeling the evolution ofantiproton intensity in the Recycler assuming injections from the Tevatron andAccumulator. At the beginning of each collider cycle the Recycler contains theantiprotons recycled from the Tevatron. Every hour after the start of a collider storeantiprotons stacked in the Accumulator are injected into the Recycler. It is assumed thatthe stacking rate is 20x1010 antiprotons/hour.

Time (Hours)

Rec

ycle

r In

tens

ity (

E9)

140

160

180

200

220

240

260

280

0 2 4 6 8

Figure 2.5.1: Assuming beam intensity lifetimes of infinity (top), 500,200, 100, 50, 20, and 10 hours (bottom), evolution of the antiprotonsinjected from the Tevatron (recycled) and the Accumulator (stacked).

Beam Lifetime (Hours)

Ant

ipro

ton

Surv

ival

50%55%60%65%70%75%80%85%90%95%

100%

10 100 1000

Figure 2.5.2: Fraction of the injected antiprotons (both recycled andstacked) which survive to the start of the next Tevatron Collider store.


The results of this model, for a range of beam intensity lifetimes, are displayed infigure 2.5.1. Note that using a criterion in which 95% survival is satisfactory over the8 hours between the start of Tevatron Collider stores, it is evident that beam intensitylifetimes of 100 hours or greater are required in the Recycler. Integrating each of thesecurves, the percentage of recycled and stacked antiprotons available for luminositygeneration in the next Tevatron Collider store can be calculated. The results of theseintegrations are shown in figure 2.5.2. Again, it is evident that a beam intensity lifetimeof 100 hours or greater is necessary to support the antiproton storage mission of theRecycler.

2.5.2. Ion Trapping Requirement

The relativistic antiproton beam in the Recycler is composed of individual antiprotonswhich periodically collide with electrons circulating around residual atoms in the vacuumchamber. These electrons rebound away from the atoms with approximately 2 eV ofkinetic energy [P. Zhou, Ph.D. thesis, 1993]. The momentum transfer to the ionizedmolecules is negligible. Because the ions are positively charged, they are attracted by theantiproton beam. In fact, because the ions are necessarily formed inside the transversepotential well of the antiproton beam, they will be trapped. Unless some mechanism isintroduced to eliminate these trapped ions, the ion density will increase until it is equal tothe beam density.

The rate at which the ion density increases Ri is determined by the equation[M. Reiser, "Theory and Design of Charged Particle Beams", pg. 273]

Ri = ng nb σi v , (2.5.1)

where ng is the gas density, nb is the beam density, σi is the ionization cross-section, andv is the beam velocity. The standard relationship between the gas density and the partialpressure P of the gas in question is

ng[m−3] = 3.54x1022 P[Torr] . (2.5.2)

The ionization cross-section depends on the velocity of the beam and the atomicproperties of the gas in question. In the case of the Recycler the equation used tocalculate the cross-section can be written in the approximate form

σi[m2] = 1.9x10−24 A1 Ln 7.5x104 A2 γ 2( ) −1 , (2.5.3)

The parameters A1 and A2 are molecule specific. The value of γ is 9.45 at a kineticenergy of 8.000 GeV. The results of calculations of ionization cross-section are listed intable 2.5.1.


Table 2.5.1: Values of the parameters A1 and A2 [M. Rudd, et. al., Rev.Mod. Phys. 57, 965 (1985)] and the cross-sections themselves of relevantgasses in the Recycler vacuum system.

Gas A1 A2 σi [m2]H2 0.71 2.5 2.1x10-23

N2 3.8 0.52 1.0x10-22

CO 3.7 0.54 1.0x10-22

Assuming a peak Recycler antiproton intensity of 4x1012 in a circumference of3.3 km, the peak longitudinal beam density λb is 1.2x109 antiprotons/m. The beamvelocity is 3x108 m/s. Therefore, given assumptions justified later in this section for thevacuum partial pressures, the rate at which the longitudinal ion densities are growing canbe calculated. The results of these calculations, and the estimation of the time it takes forthe ion density to equal the beam density, are listed in table 2.5.2.

Table 2.5.2: Ion production rate calculations based on partial pressurepredictions and an antiproton beam intensity of 4x1012. The neutralizationtime of the beam for each gas does not assume the existence of the othergas.

Gas Pressure[nTorr]

Gas Density[m-3]

IonizationRate [m-1 s-1]

NeutralizationTime [s]

H2 0.1 3.5x1012 2.6x107 46CO+N2 0.002 7.1x1010 2.6x106 460

The average transverse rms beam size σr in the Recycler is 2.3 mm. Given aGaussian transverse beam distribution and longitudinal density λb the beam density isdescribed by the equation

nb(r) = λb

2π σr2 exp − r2

2σr2

. (2.5.4)

Therefore, the peak density at the beam center is 3.5x1013 antiprotons/m3. If the beamhas been neutralized to an ion density equal to the beam density, then usingequation 2.5.2 we know that the effective peak pressure seen by the beam due to thetrapped ion cloud is 3.5x1013 molecules/m3, or a pressure of 1 nTorr. This calculation isan over estimate, since it ignores the fact that trapped ions can become multiply ionized,thereby neutralizing the space charge of the beam with fewer ions.

The pressure implication of the neutralized ion cloud around the antiproton beam willbecome evident later in the section. There are two other effects from these ions. First, acoherent instability can develop due to the electromagnetic coupling between thetransverse oscillations of the antiprotons and those of the ions. Second, the ions willinduce an incoherent tune spread due to the static transverse electrostatic field generatedby the ion cloud.


The ion cloud has the same transverse dimensions as the beam, since the probabilitydensity of ionization has the same profile as the transverse beam density distribution.Therefore, equation 2.5.4 also describes the ion cloud density distribution. The radialelectric field Er generated by this distribution is

Er (r) = eλb2π εo r

1 − exp − r2

2σr2

, (2.5.5)

where εo is the free space permittivity 8.854x10-12 F/m. The radial space charge force Fris found by plugging equation 2.5.5 in the Lorentz equation to obtain

Fr (r) = e2 λb2π εo r

1 − exp − r2

2σr2

. (2.5.6)

At a radius small compared to the rms cloud radius this equation reduces to

Fr (r) = e2 λb

4π εo σr2 r . (2.5.7)

But this is the same force equation as found in either the horizontal or vertical plane of aquadrupole magnet. Converting this result into the form of a quadrupole gradient error∆K yields the result

∆K = e2 λb

4π εo σr2

1Pov

= ro λb

γβ2( )σr2

, (2.5.8)

where Po is the antiproton beam momentum, ro is the classical radius of the proton1.53x10-18 m, and the quantities γ and β are the relativistic beam energy and velocityrespectively (with the respective values of 9.45 and 0.9945). Plugging in all of thenumber expressed so far for the factors in the rhs form of equation 2.5.8 yields a spacecharge gradient of 3.7x10-5 m-2.

The tune shift ∆ν due to this gradient error is expressed as

∆ν = 14π

β(s)∆K ds∫ , (2.5.9)

where the integral is evaluated around the circumference of the ring. Assuming aconstant average beta function βave around the ring of 30 m, substituting equation 2.5.8into equation 2.5.9 yields the result


∆ν = ro λb

γβ2( )σr2

βave C4π

= 3ro λb C2πβ εN

, (2.5.10)

where C is the circumference of the ring and εN is the normalized 95% emittance. Thevalue of the peak tune shift at the antiproton beam intensity of 4x1012 and fullneutralization is 0.29, a value which is approximately two orders of magnitude too largefor a stored beam. Therefore, it is imperative to employ methods for eliminating ionsfrom the beam.

Three methods are planned for the Recycler. The first is the use of a coherenttransverse beam closed orbit oscillation at the resonant frequency of the ion oscillationabout the beam centroid. The transverse dampers installed in the Recycler to combatcoherent instabilities are planned to have electronics capable of exciting this closed orbitoscillation, just as in the Accumulator. The second is to maintain a gap in thelongitudinal beam distribution to destabilize the ions. This requires the constant use of aset of barrier bucket pulses to maintain an empty section of beam azimuth. The third is toemploy clearing electrodes to sweep away ions from the beam potential well. In theRecycler there are two beam position monitors in each half cell which will be used asclearing electrodes.

2.5.3. Ion Clearing with a Longitudinal Gap in the Beam

Maintaining a gap in the beam distribution destabilizes low mass ions due to the factthat the time periodicity of the instantaneous beam current has the same effect on the ionsas if the ions were circulating in a circular accelerator experiencing a comparable lattice.Assume that the beam is not neutralized, and that the ions have thermal kinetic energies.Then only the electric field from the beam has a significant impact on the ion motion.Equation 2.5.7 describes the radial force due to electric field of the antiproton beam.Since this force is attractive, an ion of mass M undergoes a radial oscillation about thebeam centroid described by the differential equation

˙z + e2 λb

4π εo σr2 M

z = 0 . (2.5.10)

Let ωi be the ion angular frequency indicated in this harmonic oscillator equation. At theantiproton intensity of 4x1012 molecular hydrogen H2 has a ion angular frequency of4x106 rad/s. At this rate the small amplitude H2 ion undergoes 7.13 transverseoscillations for every one antiproton revolution around the Recycler. If Tb is the lengthof the beam distribution and Tg is the length of the gap, then the matrix equationdescribing the one-turn map of the ion coordinates (z,v) is

z

v

n+1

=cos ωiTb( ) 1

ωisin ωiTb( )

−ωi sin ωiTb( ) cos ωiTb( )

1 Tg

0 1

z

v

n

. (2.5.11)


The stability of the ions is determined by the condition that the trace of the one-turnmatrix

cos ωiTb( ) Tg cos ωiTb( ) + 1ωi

sin ωiTb( )

−ωi sin ωiTb( ) cos ωiTb( ) − ωiTg sin ωiTb( )

(2.5.12)

be

cos ωiTb( ) − 12 ωiTg sin ωiTb( ) ≤ 1 . (2.5.13)

Let A = ωiTg/2 and φ = ωiTb. The magnitude of this equation for various choices of Aover the full 2π range of φ is shown in figure 2.5.3. Note that the ion motion is unstablewhen the curve is greater than unity. Since φ depends critically on the precise beamintensity, it is very hard to control accurately enough to always guarantee that the it is in aregion of instability. On the other hand, for values of A of approximately 5 or greater, theion is generally unstable independent on the detailed beam intensity.

φ/2π

cos

- A

sin

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Figure 2.5.3: Map of equation 2.5.13 for various choices of the definedparameter A over the full 2π range of φ. The values for A are 5 (top), 2, 1,0.5, 0.2, and 0.1 (bottom).

For the case again of molecular hydrogen H2, the value of A for a 2 µsec long ionclearing gap is 5. For the minimum operational current when only the recycled beam isin the accelerator A drops to 2 for the same size clearing gap. As will be seen in thesections on intrabeam scattering and stochastic cooling, it is desirable to compress thebeam longitudinally as much as possible, to at most half of the Recycler circumference.Under these conditions with only recycled antiprotons the factor A is again greater than11. For stacking from an empty Recycler, assuming transfers of intensities greater thanor equal to 2x1011 antiprotons, if the 1.6 µsec beam pulse length from the Accumulator ismaintained with barrier buckets the minimum value for A is greater than 6. On the other


hand, with an atomic number of 28, either CO or N2 are almost always expected to bestable in the presence of the ion clearing gap.

For unstable ions the growth rate of their oscillation amplitudes about the beam is

τ = To

cosh−1 cos ωiTb( ) − 12 ωiTg sin ωiTb( )( ) , (2.5.14)

where To is the revolution period of the antiprotons in the Recycler. For values of A andf where the beam motion is unstable the value of the growth rate is calculated and plottedin figure 2.5.4. Note that the for most of the phase space the growth time isapproximately equal to the revolution period.

φ/2π

Gro

wth

Tim

e (n

orm

aliz

ed to

the

Rec

ycle

r re

volu

tion

peri

od)

0123456789

10

0 0.2 0.4 0.6 0.8 1

Figure 2.5.4: Map of equation 2.5.14 when the beam motion is unstable.The values for A are 5 (bottom), 2, 1, 0.5, 0.2, and 0.1 (top).

If it is assumed that the ion amplitude growth time is also the characteristic time ittakes for the ion to be cleared from the beam, then the equilibrium ion longitudinaldensity λi is described by the equation

λi = Riτ . (2.5.15)

For the case of τ=To and the value of Ri for H2 listed in table 2.5.2, the equilibrium ionlongitudinal density is 291 H2 ions/m! It should be pointed out that larger amplitude ionssee a net field which is different from that assumed in the above linearized theory. In thecases of marginal growth linearized growth rates the net reduction in focusingexperienced by the ions may slow down or even halt their escape from the beam.


2.5.4. Ion Clearing with Clearing Electrodes

In the case of H2 where φ and A do not lead to unstable oscillations around theantiproton beam, and for the case of CO and N2 in general, another method of ionclearing is required. This is the purpose of the clearing electrodes. A pair of clearingelectrodes on opposite sides of the vacuum chamber with opposite voltage generate atransverse electric field. When that electric field is greater than the maximum radialelectric field generated by the beam, any ions between the electrodes are stripped awayfrom the beam.

The electric field generated by the beam is described by equation 2.5.5. Taking thederivative of the electric field with respect to radius and setting the result equal to zero,the radius at which the electric field is maximum is calculated to be

rmax = 1.585 σr . (2.5.16)

Substituting this result into the electric field equation yields the result

Emax = 0.45e λb2πεo σr

. (2.5.17)

With an antiproton intensity of 4x1012 in the Recycler, the maximum radial electric fieldis found to be 675 V/m. The largest effective separation d of the clearing electrodesacross the vacuum chamber is 9.5 cm. The minimum voltage across the electrodes isrelated to this separation and the maximum radial electric field according to

Vmin = Emax d . (2.5.18)

Plugging in the above number, the minimum voltage per electrode is approximately 32 V.The ions are traveling with kinetic energies determined by their temperature, which is

equal to room temperature 300°K. Table 2.5.3 contains a summary of the ion velocities,and for future reference when ion propagation in the gradient magnets are discussed theircyclotron orbit in a 1.5 kG magnetic field.

Table 2.5.3: RMS thermal ion velocity and rms cyclotron orbit radius as afunction of gas species assuming room temperature. The cyclotron orbitradius assumes the 1.5 kG magnetic field in the Recycler gradientmagnets. The overvoltage is the amount of additional voltage required toaccelerate an rms ion into the negative electrode, thereby eliminating theion from the beam.

Gas AtomicMass

rms Velocity[m/s]

rms CyclotronRadius [mm]

Overvoltage[V]

H2 2 1113 0.15 0.0013CO+N2 28 297 0.58 0.0013

In order to assure that the ions leave the beam while they ballistically traverse theclearing electrodes, an additional accelerating voltage greater than the above 32 V is


necessary. The electrodes are 1' long. Assume that a particle traveling at the rmsvelocity straight down the center of the vacuum chamber must be deflected enough tostrike the negative electrode. The additional voltage required per electrode for eachspecies of gas to perform this task is listed in the right most column of table 2.5.3. It istruly negligible.

Table 2.5.4: Mean free path calculation assuming the effective moleculardiameter to be 2x10-10 m. The point of this calculation is to verify that theion motion in the beam is ballistic in nature, since the mean free path ismuch longer than the vacuum chamber and the distance between clearingelectrodes.

Gas Pressure[nTorr]

Gas Density[m-3]

Mean FreePath [m]

H2 0.1 3.5x1012 2.3x106

CO+N2 0.002 7.1x1010 1.1x108

As shown in table 2.5.4, the motion of ions is not significantly affected by other ionsin the range of pressure that is found in the Recycler vacuum system. Therefore, it is notunreasonable to assume that a molecule ionized in the beam will travel unmolestedlongitudinally with an rms speed listed in table 2.5.3. This geometry, with theapproximate relative geometry between two clearing stations in a Recycler half cell, isshown in figure 2.5.5.

Figure 2.5.5: Sketch of an ionized molecule with an initial longitudinalvelocity in a geometry very similar to that inside a Recycler half cell.

The clearing electrodes act as a black hole, eliminating every ion that traverses them. Ifthe distance between the clearing electrodes is Lce, and the rms velocity of an ion is σv,then the average time τ it takes an ion heading toward a particular electrode to beeliminated from the beam is

τ = Lceσv

. (2.5.19)

Plugging this result into equation 2.5.15 yields an estimate of the equilibrium averagetrapped ion density between the clearing electrodes. Using previously present values forthe relevant parameters, the calculations this average ion density for each gas species islisted in table 2.5.5. The worst case density is 10,000x lower than expected atneutralization.


Table 2.5.5: Calculation of the equilibrium ion longitudinal densityassuming a distance between clearing stations of 6 m.

Gas ClearingTime [ms]

Ion Density[m-1]

H2 5.3 1.4x105

CO+N2 20 5.2x104

The Recycler vacuum system also has gradient magnets. When a gas molecule isionized inside the magnet, the ions do not simply propagate out at their thermalvelocities. As shown in table 2.5.3, the ions execute very tight horizontal cyclotronoscillations around the magnetic field lines. If these magnets were pure dipoles, the onlymechanism for ion transport to the clearing electrodes would have been ExB driftgenerated by the space charge radial electric field of the beam. At the radial fieldmaximum of 675 V/m, for a relatively improbable ion more than a sigma away from thebeam center, the drift velocity is 675 / 0.15= 4500 m/s. But the small amplitude ions seean order of magnitude smaller electric field, and for the case of low beam intensity theelectric field is yet again another order of magnitude smaller. On the other hand, that stillleaves a factor of 100x lower density than expected if the beam were completelyneutralized. But this is the factor of 100x that was needed to reduce the tune spreadeffects of the ion cloud to manageable levels.

In addition, the gradient portion of the Recycler bend magnets introduce ∇B drift.As an ion executes horizontal cyclotron orbits, the gradient in the dipole field causesthese orbits to have a horizontal position dependent radius of curvature. This causes theparticle to drift longitudinally. The drift velocity vd depends on the cyclotron radius rc,the field gradient g, and the cyclotron frequency fc according to the equation

vd = π f c g rc2 . (2.5.20)

Table 2.5.6 contains the results of this calculation for the gas species of interest. Thegradient for the normal cell Recycler gradient magnets is 2.5 m-1. Note that compared tothe neutralizing ion density of 1.2x109 m-1, the H2 density in the magnet is almostunaffected whereas the CO+N2 density is a factor of 20x below neutralization. Takinginto account the fact that the gradient magnets make up approximately half of the ring,this indicates that with clearing electrodes only that CO+N2 neutralization can beavoided. The combination of a gap and electrodes seems to be needed for H2.

Table 2.5.6: Calculation of the equilibrium ion longitudinal density in agradient magnet assuming ∇B drift as the mechanism for trapped ion loss.The expected average equilibrium ion densities in the magnets are alsocalculated.

Gas CyclotronFreq. [MHz]

Drift Speed[m/s]

Magnet IonDensity [m-1]

H2 1.1 0.19 5.2x108

CO+N2 0.082 0.22 5.2x107


2.5.5 Vacuum Specification

The beam tube vacuum pressure requirement is determined by antiproton intensitylifetime, antiproton emittance growth, and ion trapping considerations. The emittancegrowth rates should be small compared to the anticipated intrabeam scattering growthrates. The intensity lifetime should be long enough insure that the stacking rate necessaryto achieve the required antiproton intensity is not increased by more than a few percent.Because vacuum pressures always improve with time, the specification quoted in thissection will apply to the initial pressure needed for reasonable operations.

The transverse normalized 95% emittance growth rate is determined by multipleCoulomb scattering with the nuclei of the residual gas in the beam tube. Assuming arelativistic beam, the equation describing this growth rate can be written as

εn =3 βγ r

15 MeV

mc2

2 cLrad

, (2.5.21)

where <β> is the average beta function of the accelerator, γr is the relativistic energy ofthe beam, and Lrad is the radiation length of the gas at a given temperature and pressure.Radiation length values at standard temperature (0 °C) and pressure (760 Torr) are listedin table 2.5.7.

Table 2.5.7: Radiation lengths for the two constituent moleculescommonly found in a high vacuum stainless steel system such as thatexpected for the Recycler ring.

GasRadiation

Length(g/cm2)

Density@STP(g/l)

RadiationLength

(m)

H2 61 0.090 6800CO+N2 38 1.25 300

Table 2.5.8: Normalized 95% emittance growth rate for each componentgas in a high vacuum system assuming a total pressure of approximately1 nTorr and a standard ratio of 5:1 between hydrogen and nitrogen/carbonmonoxide.

GasPartial

Pressure(nTorr)

RadiationLength

(m)

EmittanceGrowth Rate(π mmmr/hr)

EmittanceGrowth

Time (hrs)H2 0.1 5.2x1016 0.05 200

CO+N2 0.002 6.0x1015 0.05 200

Assuming an average beta function value of 30 m and a kinetic energy of 8 GeV, theemittance growth rates for the same constituent vacuum gasses are listed in table 2.5.8.Note that the measured and expected ratio of hydrogen to nitrogen/carbon monoxide isset at 50:1. As will be shown later, these pressures are the result of measured outgassing


rates and calculated pumping speeds. In order to calculate an emittance growth time, abase emittance of 10 π mmmr is assumed.

The stochastic cooling system is anticipated to have an emittance cooling time ofapproximately 4 hours. From table 2.5.8 it is can be shown that maintaining an averageCO+N2 partial pressure of less than 0.1 nTorr is necessary for Recycler operations.

Table 2.5.9: Nuclear interaction lengths for the two constituent moleculescommonly found in a high vacuum stainless steel system.

GasNuclear Int.

Length(g/cm2)

Density@STP(g/l)

NuclearInteractionLength (m)

H2 51 0.090 5700CO+N2 88 1.25 704

Table 2.5.10: Intensity lifetime due to nuclear interactions with eachcomponent gas in a high vacuum system.

GasPartial

Pressure(nTorr)

NuclearInteractionLength (m)

AntiprotonLoss Time

(hrs)

AntiprotonLoss Rate(1010/hrs)

H2 0.1 4.3x1016 40,000 0.0063CO+N2 0.002 1.4x1017 250,000 0.0010

The other consideration is particle lifetime. The two mechanisms which removeparticles from the ring are nuclear interactions and large angle Coulomb scattering(Rutherford scattering). Nuclear interactions are typically broken down between elasticand inelastic scattering. Though a portion of the elastically scattered particles would stayin the accelerator, it is easier to take the worst case assumption that they are all lost. Inthat case the total cross-sections, characterized as a nuclear interaction length, is used.Table 2.5.9 contains the nuclear interaction lengths for the expected constituent gasses inthe vacuum tube. In table 2.5.10 the lifetime and particle loss rates are calculated using abase intensity of 250x1010 antiprotons in the Recycler.

Single large angle Coulomb scattering angles greater than the angular acceptance ofthe Recycler occur with a frequency described by the equation

σel =2π rp

2 Z2

γ r2

βy

Ay. (2.5.22)

The lifetime associated with this cross-section is

τel = 1ngas σel βc

, (2.5.23)

and rp=1.535x10-18 m. The results of these calculations are listed in table 2.5.11.


Table 2.5.11: Intensity lifetime due to large angle Coulomb scattering.

GasPartial

Pressure(nTorr)

Cross-Section

(mbarns)

AntiprotonLoss Time

(hrs)

AntiprotonLoss Rate(1010/hrs)

H2 0.1 17 30,000 0.008CO+N2 0.002 870 30,000 0.008

In conclusion, even though its partial pressure is lower than the hydrogen, the CO+N2 iscomparable in both the particle loss and the emittance growth rate. A partial pressure lessthan 1x10-10 Torr is desirable for those species.

2.5.6. Outgassing of Stainless Steel

The spacing and pumping speed of the lumped ion-sputter and titanium sublimationpumps in a traditional Fermilab system is determined by the outgassing rate of gasmolecules from the surface of the stainless steel vacuum tube. Because the cost of thevacuum system scales with the number of pumps, minimizing this outgassing rate is verydesirable.

Upon chemically cleaning a stainless steel tube and performing a 150°C bake aftersystem assembly, a hydrogen surface outgassing rate of 1x10-12 T-l/cm2-sec isachievable. At this point the only other gas in the system is CO+N2, which comesdominantly from the ion pumps and ion gauges. The hydrogen comes from diffusion ofmolecules out of the bulk of the stainless steel material. The key to reducing the cost ofthe Recycler vacuum system is to eliminate this bulk hydrogen.

High concentrations of hydrogen exist in stainless steel because of one step in it'sproduction, when the steel is quenched in a hydrogen atmosphere. It has been found[R. Calder and G. Lewin, Brit. J. Appl. Phys. 18, 1459 (1967)] that the hydrogen can beremoved by heating the stainless steel in a good vacuum (<10-6 Torr) at a temperature ofapproximately 500°C. Using this technique, measurement results at Fermilab with a30 m test vacuum system have found surface outgassing rates of 2x10-13 T-l/cm2-sec,even though it turns out that the ultimate pressure during the bake was only 10-3 Torr andmultiple vacuum accidents during studies. More details concerning the hydrogendegassing oven and its operation can be found in chapter 3.

The calculation of time and temperature vs. hydrogen degassing of stainless steel israther straightforward. Assume that an infinite slab of stainless steel of thickness d isplaced in a perfect vacuum and heated to some temperature T. The one dimensionaldiffusion equation describing this situation is

D∂2c

∂x2 = ∂c∂t

. (2.5.25)

The diffusion coefficient D as a function of some typical outgassing temperatures isplotted in figure 2.5.6. The initial condition is that the stainless steel is uniformlysaturated with hydrogen at some initial concentration co. As compared to an atmospherichydrogen concentration of 1.4x10-4 T-l/cm3, the initial concentration found in 300 series


austentic stainless steels is 0.3 T-l/cm3. Outside of the slab it is assumed that a perfectvacuum exists. The solution of the differential equation with these boundary conditionscan be written in terms of an infinite sum

c(x, t) = co4π

12n + 1( )

n=0

∞

∑ sinπ 2n + 1( )x

dexp − π 2n + 1( )

d

2Dt

. (2.5.26)

Temperature (°C)

Dif

fusi

on C

oeff

icie

nt (

cm2/

sec)

1.00E-141.00E-131.00E-121.00E-111.00E-101.00E-091.00E-081.00E-071.00E-061.00E-051.00E-04

0 200 400 600 800 1000

Figure 2.5.6: Hydrogen diffusion rate as a function of temperature instainless steel. The data points are at typical degassing temperatures. Thelines are for the purpose of interpolation.

Position in Material (cm)

Hyd

roge

n C

once

ntra

tion

00.10.20.30.40.50.60.70.80.9

1

0 0.03 0.06 0.09 0.12 0.15

Figure 2.5.7: Hydrogen concentration profile across the beam tube wall asa function of time at 500°C. In the beginning the concentration is uniformand scaled to unity. The curves show the concentration profiles after60 sec, 10 minutes, and 1 hour. After 3 hours the concentration is 1x10-7.


Time at 500°C (sec)

Out

gass

ing

Rat

e (a

rb.)

0.00001

0.001

0.1

10

1000

1 10 100 1000 10000

Figure 2.5.8: Hydrogen outgassing rate after cooldown as a function of thetime spent at 500°C for degassing.

For the case of Recycler vacuum chamber, using a diffusion coefficient of 1x10-6 cm2/sec(500°C) and a thickness d of 0.065" (approximately 1.5 mm), the concentration profilethrough the vacuum tube wall as a function of position in the wall and time attemperature is plotted in figure 2.5.7.

The surface outgassing rate σq of hydrogen from either surface is simply thederivative of the hydrogen concentration at the surface times the diffusion coefficient

σq (t) = D∂c∂x

x=0

= 4coDd

exp − π 2n + 1( )d

2Dt

n=0

∞

∑ . (2.5.27)

Figure 2.5.8 contains a plot of the surface outgassing rate after cooldown as a function oftime the vacuum tube was degassed at 500°C. The plan is to bake the tubes at 500°C for6 hours with an oven pressure less than 1x10-6 Torr to guarantee full degassing.

2.5.7. Pressure Calculations

The pressure P(z) at some azimuth z around the ring is calculated using thedifferential equation

cd2P

dz2 − s P = −q , (2.5.28)

where c(z) is the specific conductance of the vacuum tube, s(z) is the linear pumpingspeed, and q(z) is the specific outgassing rate. If these coefficients of the differentialequation are piecewise constant, then the solution in any section of vacuum tube is


P(z) = A expsc

z

+ Bexp − s

cz

+ q

s. (2.5.29)

Just as in the case of dispersion function lattice calculations, this solution lends itself tomatrix calculations on the basis vector (P,Q,1), where Q(z) is the flow rate of gas downthe tube at the azimuth z.

In a lumped stainless steel system the pumps and beam tubes are treated as separable(similar to the concept of separated function magnets). Therefore, in a vacuum tube thepumping speed is zero. The specific conductance of the elliptical cross-section beam tubecan be written as

c m − l / s[ ] = 1.30a cm[ ] b cm[ ]( )2

a2 + b2

T °K[ ]300

28M

, (2.5.30)

where a and b are the half width and half height of the inside surface of the vacuum tube,T is the temperature of the system, and M is the atomic mass of the gas molecules (theequation is referenced to room temperature and the atomic mass of nitrogen).

Table 2.5.12: Parameters expected to describe the vacuum system in theRecycler ring. This spacing corresponds to three 30 liter/sec pump (eitherion or titanium sublimation) per half cell, where the pumping speed(assuming ion pumps) was derated to account for saturation and lowpressures at the pump.

Parameter H2 CO/N2Lumped Pump Pumping Speed (L/s) 30 10Surface Outgassing Rate (T-L/s-cm2) 2x10-13 1x10-15

Distance between Lumped Pumps (m) 5.75 5.75Total Width of Elliptical Pipe (inch) 3.75 3.75Total Height of Elliptical Pipe (inch) 1.75 1.75Molecular Mass of the Gas 2 28Specific Conductance (m-L/s) 100 28Specific Outgassing Rate (T-L/s-m) 4.4x10-10 2.2x10-12

Pressure at Lumped Pumps (nTorr) 0.084 0.0013Pressure Halfway between Pumps (nTorr) 0.100 0.0016Average Pressure (nTorr) 0.096 0.015

To convert from the surface outgassing rate σq to the specific outgassing rate q it isnecessary to multiply σq by the surface area per unit length. For an elliptical beam pipe

q[T − l / s − m] = 100π 2(a[cm]2 + b[cm]2 ) σq[T − l / s − cm2] . (2.5.31)

Table 2.5.12 contains an example of typical parameter values used for calculating theRecycler vacuum performance. The ion pumps to be used are 30 liter/sec pumps, but theactual pumping speeds are derated because of the low pressures and assuming that the


pumps are nitrogen saturated during pumpdown. The majority of the pumps are of thetitanium sublimation variety, which have much lower ultimate pressure and much highertypical pumping speeds. The present titanium sublimation pumps are also planned tohave a speed of 30 liter/sec. Figures 2.5.9 and 2.5.10 show the dependence of pressure onposition in the beam tube. Note that the average pressures described are much lower thanassumed in the lifetime discussions above.

Distance Along Vacuum Chamber (m)

Pres

sure

(nT

orr)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 0.5 1 1.5 2 2.5 3

Figure 2.5.9: Hydrogen partial pressure as a function of distance along thevacuum tube. The origin is the symmetry point halfway between any twopumps. The parameters which generated this figure are listed intable 2.5.12. The horizontal line designates the average pressure.

Distance Along Vacuum Chamber (m)

Pres

sure

(nT

orr)

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0 0.5 1 1.5 2 2.5 3

Figure 2.5.10: CO+N2 partial pressure as a function of distance along thevacuum tube. The origin is the symmetry point halfway between any twopumps. The parameters which generated this figure are listed intable 2.5.12. The horizontal line designates the average pressure.


2.5.8. Magnetic Shielding

There are many sources of time-dependent magnetic fields which if left unshieldedwould modulate the closed orbit position and tune of the Recycler beam. Therefore, ithas been decided to generate a hermetic seal of magnetic shielding around the Recyclervacuum chamber. In order to save money the insitu bake insulation and the magneticshielding have been merged into the same effort. Because of this link to the insituinsulation, and because of the need to integrate the shielding with the vacuum fabrication,magnetic shielding is one of the responsibilities of the vacuum Recycler group. A sketchof the geometry of the magnetic shielding and insitu bake insulation is displayed in figure2.5.11. The regions of vacuum chamber occupied by magnets do not require shieldingdue to the thick flux return they employ.

Stainless SteelVacuum Chamber

Insitu BakeInsulation

Soft Iron

Mu-metal

Figure 2.5.11: Sketch of the integrated magnetic shielding and insitu bakeinsulation for the Recycler ring.

.The dominant sources of stray time-dependent magnetic fields at the Recycler tunnel

position are:

1) Main Injector magnet fringe fields. These have been measured to be nomore than 2 Gauss at the Recycler position [A. Mokhtarani & P.Mantsch, MTF-94-0052 (1994)].

2) Main Injector magnet bus bypasses. By calculating the dipole fieldgenerated by a pair of busses near the wall at the Main Injectorelevation, a maximum field of 2 Gauss is calculated.

3) Uncompensated quadrupole loop current. The focusing and defocusingquadrupole circuits are each single loops around the tunnel.Therefore, the net current difference between these loops willgenerate a net magnetic flux through the wetland inside the MainInjector. More important, it would generate approximately 4Gauss at the Recycler beam pipe.


4) High current cables in trays. One example would be Lambertsoncables. Estimates generate fields as high as 5 Gauss.

In order to firm up these estimates and to identify any unanticipated source of field, a fluxmeasurement experiment is being designed for the Main Ring tunnel at the comparableelevation of the Recycler. Another purpose of this test is to measure the actual fieldattenuation one obtains from magnetic shielding. There is some doubt as the validity ofmore detailed calculations of magnetic shields in the milliGauss field range. It is becauseof these doubts that only semi-quantitative calculations are presented below.

A system capable of shielding the beam to an extent comparable to the dipole fieldstrength criterion is necessary. The fields in the gradient magnets is specified to have amaximum allowable error of 5x10-4 in a field of 1.5 kG. This corresponds toapproximately 1 Gauss over roughly 4 m. In order to assure that systematic or randomeffects from the time dependent fields are negligible, especially in alignment sensitiveregions such as the stochastic cooling pickups, a stray field goal at the Recycler beam of10 mG has been specified.

Figure 2.5.12: Sketch of magnetic field lines from the tunnel being drawninto the soft iron shield around the beam pipe. Note that due to the finitepermeability of the iron, approximately 0.1% of the flux continues throughto the beam.

When a layer of soft iron is wrapped around an otherwise non-ferric material such asthe beam pipe, the higher permeability of the iron pulls magnetic flux lines from an area


approximately double the width of the iron geometry. In the case of the Recycler, thiscovers an area almost 8" across. The plan is to use a layer of soft iron which is 6 milsthick. Therefore, the peak magnetic field in the soft iron is approximately 670 timeslarger than the ambient field. Since the saturation field of the soft iron is 20 kG, this putsan upper limit on the magnetic field at the Recycler of 30 Gauss. This is 5-10 timeshigher than anticipated. In specific locations in which there are known or discoveredhigh magnetic field generating devices, extra shielding can be added to prevent the softiron from going into saturation.

The problem with the above solution is that even when not in saturation, the soft ironhas a finite permeability of approximately 3000-5000. Therefore, some fraction of theambient tunnel magnetic flux still penetrates to the beam. For time-dependent fields themaximum level of attenuation is approximately 1000x. It is for this reason that mu-metalis inserted as an addition layer between the beam pipe and the soft iron.

The disadvantage of mu-metal is that it's saturation level is on 8 kG. On the otherhand, it's permeability is in the range of 12,000-400,000. At fields up to 3 kG andfrequencies up to 60 Hz, field attenuation factors of 100,000x are achievable [AmunealManufacturing Corp., "Complete Guide to Magnetic Shielding"]. The plan for theRecycler is to use a mu-metal layer which is 4 mil thick. Over basically the same area,the maximum residual field inside the soft iron which the mu-metal can shield is 2 Gauss.By design, this field matches the leakage expected through the soft iron just as it beginsto seriously saturate.

The power spectrum of the magnetic fields in the tunnel below 60 Hz should bedominated by 0.5 Hz from the basic Main Injector ramp plus the first 10-100 harmonicsneeded to reproduce the more complex, non-sinusoidal current waveforms found in mostcorrectors, busses, and specialty devices (such as Lambertsons). At these frequenciesboth the soft iron and mu-metal still behave as if exposed to a constant magnetic field.

2.6. RF System

The Recycler RF system which generates the longitudinal phase space gymnasticsdescribed in section 2.1 is composed of four 50Ω gaps driven by wideband amplifiers.The bandwidth of the net system is from 10 kHz to 100 MHz. The upper cutofffrequency corresponds to a voltage rise-time or fall-time of a few nanoseconds, far fasterthan actually necessary. The low frequency cutoff is composed of two poles, one fromthe gap inductance and the other from the amplifiers. Because there is no DC response inthe system, two concerns need to be considered. The first is the amount of droop in thesquare voltage pulse during its duration. The second is the amount of baseline offsetbetween the voltage pulses which can accelerate or decelerate beam particles whichshould be drifting.

The amount of droop can be calculated fairly easily. Using a simulation program tocalculated response functions, as the two pole high pass filter response shown in figure2.6.1, the resultant accelerating voltage waveform is presented in figure 2.6.2. For pulselengths less than 1 µsec the droop is well less than 10%. This level of droop has only asmall quantitative effect on the bucket height.


1 10 100-40

-35

-30

-25

-20

-15

-10

-5

0

Frequency (kHz)

Amplitude (dB)

0

22.5

45

67.5

90

112.5

135

157.5

180

Phase

Figure 2.6.1: Two pole response function simulating the lower bandwidthlimit of the accelerating gap and power supply.

0 0.001 0.002 0.003 0.0040

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (ms)

Response (Norm.)

Figure 2.6.2: Calculation of the droop and the original pulse as a functionof time. Note that for the most part pulse lengths of 1 µsec and less areenvisioned, which infers that droops of less than 10% should be expected.

The first rule for suppressing baseline offsets is to always generate pairs of voltagepulses with equal and opposite areas, so that the net area is zero. This insures that there isno DC component in the drive signal. As can be seen in figure 2.6.3, after the pair ofpulses the baseline voltage is at zero again. But note that inside the barrier bucket thedrift region contains a nonzero residual voltage.


0 0.001 0.002 0.003 0.004-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

Time (ms)

Response (Norm.)

Figure 2.6.3: Calculation of the response to a barrier bucket pairconstraining a 1.5 µsec batch with 1 µsec voltage pulses.

Another potential problem is the total impedance of 200Ω associated with the fourgaps. The peak antiproton beam current envisioned is approximately 50 mA.Multiplying this current by the total impedance yields a beam loading waveform with apeak voltage of 10 V. Though this sounds like a small number, it is in fact enough todistort longitudinal phase space and cause a non-uniform beam distribution in the gap.

0 0.001 0.002 0.003 0.004-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

Time (ms)

Response (Norm.)

Figure 2.6.4: Calculation of the response to a barrier bucket pairconstraining a 1.5 µsec batch with 1 µsec voltage pulses, but this time witha gap feedback system in operation with a loop gain of 10.

To fix the above three concerns simultaneously a feedback loop is envisioned. Bycomparing the gap voltage and the input to the amplifiers, the error signal is amplified


and added back into the amplifier. In this way the errant voltage from the low frequencybandwidth limit and the beam loading voltage can be corrected. Figure 2.6.4 shows theresult of the inclusion of such a feedback system with a loop gain of 10. Figure 2.6.5contains a block diagram of the feedback system.

High Power Drive

RecyclerAccelerating

Gap

MI-60ServiceBuilding

Gap Monitor

Tunnel

Figure 2.6.5: Block diagram of the feedback system around eachgap/amplifier designed.

2.7. Impedances and Instabilities

Because the beam is unbunched, the instabilities which are expected to be a problemare not complicated. The two instabilities to be potentially concerned about are thetransverse resistive wall instability and the longitudinal microwave instability.

2.7.1. Impedance Budget

The dominant sources of accelerator impedance in the Recycler ring are the beamposition monitors, the kicker magnets, the accelerating cavities, and the resistance of thevacuum tube itself. At first one could assume that the impedance budgets of the MainInjector and the Recycler are the same at

Z||n

= 1.6 Ω Z⊥ = 2.2 MΩ / m .

However, the impedance will be dramatically less in the Recycler. For instance, there areno laminated Lambertson magnets, the kickers are slower and hence have a thickercoating, and there are no high-Q, high impedance RF cavities.

The beam impedance is dominated by the space-charge impedance. Calculation(K.Y. Ng) of the magnitude of this space charge impedance at a debunched beamintensity of 2.5x1012 yields the result

Z||n

= 12 Ω Z⊥ = 420 MΩ / m


2.7.2. Resistive Wall Instability

The resistive wall instability involves long wavelengths, and therefore does notdepend on whether beam is bunched or coasting. Because the Recycler vacuum tube isthe same material and cross-section as the Main Injector, the results obtained for the MainInjector for the instability growth time can simply be scaled with respect to the beamintensity. At an intensity of 1x1013 antiprotons, a growth time of approximately 3.6 ms,or 300 turns, is expected in the absence of space charge impedance or Landau damping.Note that a tune below the half integer was chosen to minimize the severity of theinstability. Calculations including the space charge impedance and Landau dampingindicate that the beam is in fact stable, and feedback systems are not necessary.

2.7.3. Microwave Instability

The minimum rms momentum spread in the Recycler will be 0.3 MeV. At thatmomentum spread the beam intensity is approximately 250x1010. The thresholdlongitudinal impedance for microwave instability is given by

Z||n

< 0.68π Zoη γ r R

N rp

σeEo

2

, (2.7.1)

where rp=1.5x10-18 m and Zo=377 Ω. Plugging in the rest of the numbers for theRecycler a threshold impedance of 70 Ω is found. The only impedance larger than this isfrom the four 50 Ω RF cavities at low frequencies below 1 MHz. If a problem did occur,the RF cavity feedback described above would suppress it.

2.8. Intrabeam Scattering

Intrabeam scattering, or Coulomb interaction between antiprotons, is the dominantheating mechanism which, when balanced against cooling forces from stochastic cooling,determines the equilibrium emittance achievable in the Recycler. Since each collisionconserves energy, it is possible that as the thermal energy of one plane increases, which isrelated to the emittance in that plane, the emittance in another plane decreases, much asthe temperatures of two heat reservoirs tend toward equilibrium. However, the potentialfor coupling some of the directed longitudinal beam energy into either longitudinal ortransverse thermal motion in general leads to an overall increase in the phase spacevolume of the beam as a result of Coulomb interactions.

From simple kinematic arguments, it is possible to show that below transition,Coulomb collisions can lead to an equilibrium between the emittances of all planes, whileabove transition no such equilibrium is possible, that is, the emittance in all planescontinues to increase. This comes about because the effective longitudinal temperature isproportional to the slip factor η, which implies a negative temperature above transition.The negative temperature is another manifestation of the negative mass instability.

Since the Recycler is well below transition, it could be expected that such anequilibrium is possible: i.e. the emittance of one plane increases while that of another


decreases. However, this is only partly true due to two mitigating factors. First, sincethere is a distribution of energies and angles among colliding particles, the transition fromequilibrium to growth conditions is gradual. A completely stationary equilibrium is onlyachievable at non-relativistic energies. Second, Mtingwa and Bjorken have shown thatthe overall phase space volume can only remain stationary if a specific condition onlattice parameters is satisfied everywhere which, in general, is usually never true for agiven lattice. Stated in physical terms, whenever Coulomb scattering occurs in thepresence of gradients, either in configuration or velocity space, work is effectively doneon the distribution, namely, emittance growth occurs.

The original work on this subject was carried out by Piwinski, and later work, basedon an alternative, but equivalent approach, was carried out by Mtingwa and Bjorken. Thelatter work is often cited, because of the generality of the analysis, however certainapproximations are typically made in the literature which do not permit immediateapplication of this analysis to beams below transition. Using the most generalexpressions from these references, it can be shown there is still some discrepancybetween Piwinski`s work and that of Mtingwa and Bjorken regarding the conditionsnecessary for thermal equilibrium. However, we have extensively studied these twoformulations and have found that the quantitative differences between these models aresmall. In the following analysis, we assume there is no transverse coupling, and that allparticle distributions are Gaussian.

RMS Momentum Spread (MeV/c)

Lon

gitu

dina

l Gro

wth

Rat

e[1

/hou

r]

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10

Figure 2.8.1: Longitudinal intrabeam scattering growth rates as a functionof transverse emittance and momentum spread. The different curves arefor transverse normalized 95% emittances of 5 (top), 10, 15, and20 π mmmr (bottom). The beam intensity was 7x1012 antiprotons.

For the Recycler, there are two regimes of interest: a relatively high momentumspread regime in which stochastic cooling is used, and a regime with small whereelectron cooling is relevant. For large momentum spread, emittance growth times areshown in figure 2.8.1.


Inverse growth rates for the longitudinal plane are plotted as a function of momentumspread for various fixed transverse emittances (normalized, 95%). In figure 2.8.2, we plotthe dependence of the horizontal scattering rates vs. momentum spread. At sufficientlysmall momentum spreads, it is possible that slight cooling of the horizontal emittance canoccur through coupling to the relatively cold longitudinal plane. Note that since we haveneglected coupling in this analysis, and there is no vertical dispersion, there is littlecoupling between the longitudinal and vertical planes. The vertical plane usually iscooled, but with very long cooling times. Hence it will be ignored in this analysis. Inthis regime, the sum of the horizontal and longitudinal inverse growth rates isapproximately constant, although the net overall phase space volume increases, due to thepresence of gradients. A small amount of longitudinal cooling is expected, as thetransverse plane heats. In the limit of small momentum spread the situation is reversedwhere the longitudinal plane is strongly heated, while the horizontal plane can bemeasurably cooled.

RMS Momentum Spread (MeV/c)

Tra

nsve

rse

Gro

wth

Rat

e[1

/hou

r]

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 2 4 6 8 10

Figure 2.8.2: Transverse intrabeam scattering growth rates as a function oftransverse emittance and momentum spread. The different curves are fortransverse normalized 95% emittances of 5 (top on right edge), 10, 15, and20 π mmmr (bottom on right edge). The beam intensity was 7x1012

antiprotons.

It should be noted that the actual equilibrium achieved is a balance between stochasticcooling and diffusion caused by scattering, all of which are non-Maxwellian processes;that is, tails will develop on the distributions as the energy-dependent diffusion and dragforces come to equilibrium in detailed balance. As such, the actual equilibrium must befound by the solution of a time-dependent Fokker-Planck approach.

It is worthwhile to note that the regime predicted for the Recycler in which somedegree of transverse cooling is possible has not yet been investigated experimentally. Itwould be valuable to carry out a series of experiments in the Fermilab Accumulator,which can access the regime below transition.


2.9. Stochastic Cooling

The stochastic cooling systems in the Recycler ring are discussed in section 2.1 andchapters 3 and 4. The general picture one acquires is that the horizontal and verticalbetatron cooling systems are not controversial and relatively straightforward. On theother hand, the momentum cooling system is critical, where cooling strength andmomentum aperture are key design parameters. In this section the system parameters forboth the betatron and momentum cooling systems are reviewed. To set the stage, theinteraction between intrabeam scattering and stochastic cooling is explored explicitlyfirst.

2.9.1. Intrabeam Scattering and Barrier Bucket Compression

The calculations of intrabeam scattering in the previous section indicate that themomentum growth rate for a fixed normalized 95% transverse emittance of 10 π mmmr isquite fast for the anticipated beam currents. In addition, the rate of increase in growthrate with diminishing rms momentum spread is very well described by the approximation

αIBS = k

σp

P

3 , (2.9.1)

where k=1.3x10-11 hr-1 at an antiproton beam intensity of 7x1012. Both the calculatedand fit dependencies of intrabeam scattering growth rate on rms momentum spread areplotted in figure 2.9.1. Assuming a stochastic cooling/intrabeam scattering model inwhich distribution shapes are constant and rms momentum spread is an adequateparameterization of the beam temperature, a cooling system with a momentum coolingtime of 1 hour can only reduce the rms momentum spread to approximately 2 MeV at thecurrent of beam intensity of 7x1012. The engineering form of the equation can be writtenas

αIBS[hr−1] = 0.093Ib [mA]

σE [MeV]( )3 , (2.9.2)

The cubic nature of the dependence of intrabeam induced growth time on rms energyspread suggests a Recycler stacking scenario in which the cooled beam distribution isalways compressed in order to maintain the largest energy spread inside the energyaperture of the momentum cooling system. This time agile compression of the azimuthaldistribution of the beam is carried out with the barrier bucket RF system.

Rough calculations [G. Jackson, MI-Note 164] indicate that a 0.5 hour momentumcooling time for a 21 mA instantaneous current antiproton beam with an rms energyspread of 2.7 MeV is sufficient for the beam distribution expected at any time in theRecycler ring during Run II.

As a result of the curve in figure 2.9.1, barrier bucket compression aimed atmaintaining a large momentum spread at the expense of higher peak current will besystematically employed in the following scenario. Because of other side benefits, such


as more efficient ion clearing due to the beam distribution gaps and the ease andflexibility of beam transfers, the RF system which generates these barrier voltage pulsesis a key component in the Recycler.

RMS Energy Spread (MeV)

Mom

entu

m G

row

th R

ate

(1/h

r)

00.20.40.60.8

11.21.41.61.8

2

0 2 4 6 8 10

Figure 2.9.1: Calculated intrabeam scattering driven momentum growthrate in the Recycler ring as a function of momentum spread. Thenormalized 95% transverse emittance is 10 π mmmr and the antiprotonintensity is 700x1010. The points are calculated values while the line isthe result of an inverse cubic fit.

2.9.2. General Considerations

The momentum cooling was chosen to be a filter cooling system. Non-overlappingSchottky bands are a requirement for this type of cooling system. The betatron coolingsystems (horizontal and vertical) do not use any filters and the Schottky bands overlapslightly. The effect of these requirements is described in the section on Bandwidthbelow.

To minimize the phase errors in the cooling system (“bad mixing”) the cooling signalis transmitted across the ring (from Q215 to Q111). Between these two locationsparticles traverse about 1/6 of the ring and accumulate approximately 1/6 of the phaseslip. The signal will be transmitted with a modulated laser signal.

2.9.3. Bandwidth

The most important design choice concerns the system bandwidth. The maximumfrequency that can be used without encountering Schottky band overlap is

∆pP

η f max To ≤ 1 , (2.9.3)

where


η = 1

γ t2 − 1

γ 2 , (2.9.4)

γt is the Recycler relativistic transition energy, and γ is the relativistic beam energy. Therevolution period To is determined mostly by the circumference of the Main Injectortunnel. The maximum cooling frequency fmax is therefore inversely proportional to themomentum spread.

The equilibrium momentum spread is determined by the balance between the coolingrate and the heating rate from external mechanisms. Intrabeam scattering is expected tobe the dominant heating mechanism longitudinally. Since stacked beam is trappedbetween two RF barriers and both the cooling and heating rate depend on the separationbetween the barriers (barrier bucket compression), the momentum spread depends on thechoice of the amount of bucket compression. However, the choice is limited by thenecessity of retaining adequate longitudinal phase space for injecting and recyclingantiprotons. For a given choice of bucket compression, the required momentum spread isdetermined by the need to maintain the loss from diffusion at a level that is smallcompared to the stacking rate. Calculations indicate that a momentum spread of ±20MeV/c will adequately retain the beam with a cooling system bandwidth of 0.5 to2.0 GHz. It is tentatively planned to achieve this bandwidth with two separate coolingsystems: one operating from 0.5 to 1.0 GHz and one operating from 1.0 to 2.0 GHz.

The transverse cooling system limitation of the maximum frequency comes from the“bad mixing” between pickup and kicker. For a momentum spread of ±20 MeV/c acooling bandwidth of 2.0 to 4.0 GHz is appropriate. The transverse heating rate fromintrabeam scattering is quite small, and the transverse emittance will probably bedetermined by other mechanisms. It is probably undesirable for the transverse emittanceto be smaller than 10π because of the increase in longitudinal intrabeam scattering thatresults from low emittance beams. On the other hand, the equilibrium emittance will notbe much less than 10 π mmmr if the beam heating rate is 1 π mmmr/hr. For this reason, amaximum beam heating rate (from all sources other than the cooling system) has beenspecified to be a maximum of 1 π mmmr/hr.

2.9.4. Stability

The gain of the longitudinal cooling system is limited by stability considerations. Ithas been assumed that errors in the gain function will limit the gain to a value 10 dBbelow the stability limit. This assumption is thought to be somewhat (but not overly)conservative in light of experience with similar systems in the Antiproton Source.

The betatron cooling systems are stable well past the optimum gain and should notpresent any unusual stability problems.

2.9.5. Simulation Description

The simulation of the stacking process is derived from the Fokker-Planck simulationused to design the momentum cooling for the Antiproton Source. The simulationassumes a coasting beam and neglects the transverse motion. The line density in thesimulation is computed from the total beam in the stack divided by the sum of the barrierbucket compression and 1/2 the pulse width. The RF stacking and unstacking are


assumed to be perfectly adiabatic and with negligible emittance dilution. The bucketheight (20 MeV) is treated as a hard aperture: particles that escape from the barrierbucket are lost.

Thus, the model used for the cooling process is exactly correct for a machine with aninfinite voltage RF barriers and a finite momentum aperture. This model should beperfectly adequate for the dense portion of the antiproton stack. However, for particlesthat have larger momentum offsets, this approximation underestimates the time spentunder the influence of the barrier and overestimates the particle density. For example, thestack is contained between two barrier voltage pulses that capture 139 eV-sec. Thesimulation, with infinite height buckets, contains only a total of 112 eV-sec.

Intrabeam scattering is incorporated in an average way with the addition of an energyindependent diffusion constant

D =2σp

2

τl, (2.9.5)

where σp is the momentum of the beam and τl is the calculated intrabeam scatteringheating time. The value of σp varies somewhat in the stacking process, but the variationis not included in the simulation. It is adequate to use the final value of σp. The value ofD is, however, scaled to account for the changing intensity of the stored beam.

The system gain function is calculated using ideal components. Gain errors areintroduced by multiplying the response function of a broad-band (Q=1) resonatorcentered at mid-band. No frequencies outside the nominal cooling band are considered:it is assumed that these frequencies contribute no net heating or cooling. The resultinggain functions are shown in figures 2.9.2 through 2.9.4.

1 4 0

1 4 5

1 5 0

1 5 5

1 6 0

1 6 5

1 7 0

1 7 5

1 8 0

- 2 7 0

- 1 8 0

- 9 0

0

9 0

- 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 5 2 0

Cooling Gain at 1.1 GHz

Mag (dB)

Phase

Ma

gn

itud

e (

dB

)P

ha

se (d

eg

ree

s)

Energy Offset (MeV)

( a )

Figure 2.9.2: Momentum cooling gain functions for the Schottky band at1.1 GHz.


1 4 0

1 4 5

1 5 0

1 5 5

1 6 0

1 6 5

1 7 0

1 7 5

1 8 0

- 2 7 0

- 1 8 0

- 9 0

0

9 0

- 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 5 2 0


Mag (dB)

Phase

Ma

gn

itud

e (

dB

)P

ha

se (d

eg

ree

s)

Energy Offset (MeV)

( b )


1 4 0

1 4 5

1 5 0

1 5 5

1 6 0

1 6 5

1 7 0

1 7 5

1 8 0

- 2 7 0

- 1 8 0

- 9 0

0

9 0

- 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 5 2 0


Mag (dB)

Phase

Ma

gn

itud

e (

dB

)P

ha

se (d

eg

ree

s)

Energy Offset (MeV)

( c )


The transverse cooling simulation is also based on a coasting beam approximationassuming that the particle momenta are constant. This assumption is not correct because:1) the momentum cooling system changes the particle momenta, 2) the beam intensityand distribution changes as the beam is stacked, and 3) the RF changes the particlemomenta. A proper calculation of the evolution of the distribution function would haveto take into account both the longitudinal and transverse degrees of freedom. If, however,the distribution function can be written as a product of distribution functions for the


longitudinal and transverse coordinates, the coasting beam approximation should beaccurate. The momentum distribution is taken from the longitudinal stacking calculationand input to the transverse calculation. The transverse cooling is calculated for particlesof a fixed momentum (but time varying density). Any new beam that is injected isassumed to have the same transverse distribution as the beam already present. The resultsof this calculation are shown below and are self-consistent with the above assumptions.

0

5 104

1 105

1.5 105

2 105

2.5 105

- 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 5 2 0

Stacked Beam DensityD

en

sity

(e

V-1

)

Energy Offset (MeV)

Figure 2.9.5: Longitudinal density profile obtained after 8 hours ofstacking.

0

0.5

1

1 .5

2

2 .5

3

3 .5

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

Integrated Stack Density

Inte

nsi

ty

(/1

01

2 )

Longitudinal Emittance (eV-sec)

Figure 2.9.6: Integrated density profile obtained after 8 hours of stacking.


The transverse heating rate (from mechanisms other than the cooling systems) iscritical. The simulation assumes that this rate is 1 π mmmr/hr. The longitudinal coolingsystem is specified to contribute less than 0.1 π mmmr/hr to the total.

2.9.6. Simulation Results

The final momentum distribution obtained is shown in figure 2.9.5. This distributionis integrated and shown in figure 2.9.6. As discussed above, the particle density isoverestimated at high values of the momentum offset.

The stack size versus time in the cycle is shown in figure 2.9.7. Also shown is thecumulative stacking efficiency: the total stack size divided by the amount of beaminjected in the current cycle. The maximum stack size is 3×1012 and the overall stackingefficiency for the cycle is about 98%.

0

1

2

3

4

5

0.9

0 .92

0.94

0.96

0.98

1

0 1 2 3 4 5 6 7 8

Stack Size

Sta

ck S

ize

(/10

12)

Cum

ulative Stacking E

fficiency

Time (hr)

Figure 2.9.7: The stack size begins at t=0 at about 1.8x1012 antiprotonsand grows to more than 3x1012 antiprotons after 7 hours of stacking. Thecumulative stacking efficiency is equal to the current beam intensitydivided by the sum of the initial beam and subsequent injections. Thecumulative stacking efficiency exceeds 98% at the conclusion of thestacking cycle.

The simulation of the cooling of transverse emittance of the beam is shown infigure 2.9.8. The initial emittance of the beam is taken to be 30 π mmmr (100%). Thebeam cools rapidly initially and then grows as the intensity increases and the cooling ratedecreases. The fraction of the beam that is contained within the 10 π mmmr emittancedesign goal is shown in figure 2.9.9. At the conclusion of the 8 hour stacking cyclevirtually all of the beam is within this emittance.


0

2

4

6

8

1 0

0 1 2 3 4 5 6 7 8

∆p=10 MeV/c∆p=0 MeV/c

Ave

rage

A2 (

π m

m-m

rad

)

Time (hr)

Figure 2.9.8: The evolution of the average amplitude-squared of the beambetatron motion. The beam emittance (95%) is approximately 3x theaverage amplitude-squared. The recycled beam cools rapidly initiallyuntil it reaches a minimum after which it grows because of the increasingintensity.

0.6

0 .65

0 .7

0 .75

0 .8

0 .85

0 .9

0 .95

1

0 1 2 3 4 5 6 7 8

∆p=10 MeV/c∆p=0 MeV/c

Ave

rage

A2 (

π m

m-m

rad

)

Time (hr)

Figure 2.9.9: The fraction of the beam contained in a 10 π mmmremittance (100%). The fraction becomes nearly 100% after 2 hours ofcooling.


- 1

- 0 . 5

0

0 .5

1

- 1 - 0 . 5 0 0 .5 1

Stability at 0.95 GHz

Im(F

G)

Re(FG)

Figure 2.9.10: Stability diagram for the Schottky bands at 0.95 GHz at7:40 (just before transfer to the Tevatron). The curve is a parametric plotof the real versus imaginary parts of the product gain (G) and beamfeedback (F) functions. The points are spaced at 0.4 MeV intervals. Thegain has been chosen so that the curve crosses the real axis at 0.3.

- 1

- 0 . 5

0

0 .5

1

- 1 - 0 . 5 0 0 .5 1

Stability at 1.7 GHz

Im(F

G)

Re(FG)

Figure 2.9.11: Stability diagrams for the Schottky bands at 1.7 GHz at7:40 (just before transfer to the Tevatron). The curve is a parametric plotof the real versus imaginary parts of the product gain (G) and beamfeedback (F) functions. The points are spaced at 0.4 MeV intervals. Thegain has been chosen so that the curve crosses the real axis at 0.3.


The stability diagrams for the two momentum cooling system bands are shown infigures 2.9.10 and 2.9.11 for the time 7:20 - just before transfer to the Tevatron. Thiscase is the one with the lowest stability margin. The stability criterion is that the curvecross the real axis with an intercept less than 1. The gain function has been scaled in thesimulation so that the stability curve passes through the point (0.30,0.0). The stabilitymargin, particularly in the lower band, is sensitive to phase errors in the gain function.However, it is believed that the designed stability margin is large enough thatunanticipated phase errors can be tolerated.

The stability criterion as stated is actually unduly restrictive in that it is sufficient butnot necessary. However, the more general stability criterion is not of practicalimportance for these systems.


2.9.7. Specifications: Longitudinal

The specifications for the momentum cooling system are given in Table 2.9.1.

Table 2.9.1: Momentum Cooling System Specifications

Band 1 Band 2Pickups (PU)Beta Function at PU 35 35 mBeam Transverse Emittance 10 10 π mmmrBeam Size 22.68 22.68 mmNumber of Pickups 16 32PU Impedance 100 100 ΩPU Gap 30 30 mmPickup Width 40 40 mmPU Sensitivity 0.84 0.84PU Combiner Loss Factor 2 2 dBNumber of Tanks 1 1PU Repeat Length 12 7 cmOverall Tank Length 2.32 2.64 mElectronicsLower Frequency 0.5 1 GHzUpper Frequency 1 2 GHzMaximum Noise Figure 1 1 dBNominal Pickup Temperature 293 293 °KNominal Electronic Gain 116 101 dBNotch Depth 30 30 dBNotch Dispersion 20 20 ppmMax Gain Ripple (Small Scale) 10 10 dBMax Gain Variation (Large Scale) 3 3 dBNominal Noise Power 2 2 WNominal Schottky Power 6 3 WNominal Total Power 8 5 WAmplified Rated (Saturated) Power 100 100 WKickersNumber of Kickers 16 32Kicker Impedance 100 100 ΩKicker Gap 30 30 mmKicker Width 40 40 mmKicker Sensitivity 0.84 0.84Kicker Loss Factor 2 2 dBNumber of Kicker Tanks 1 1Overall Tank Length 2.32 2.64 mMaximum Transverse Growth Rate 0.1 0.1 π mmmr/hr


2.9.8. Specifications: Transverse

The specifications for the betatron cooling systems are given in Table 2.9.2.

Table 2.9.2: Transverse Cooling System Specifications

Pickups (PU)Beta Function at PU 35 mBeam Transverse Emittance 10 π mmmrBeam Size 22.68 mmNumber of Pickups 32PU Impedance 100 ΩPU Gap 30 mmPickup Width 22.5 mmPU Sensitivity 0.83PU Combiner Loss (2 GHz) 2 dBPU Combiner Loss (4 GHz) 2 dBNumber of Tanks 1PU Repeat Length 4.5 cmOverall Tank Length 1.84 mElectronicsLower Frequency 2 GHzUpper Frequency 4 GHzMaximum Noise Figure 1 dBNominal Pickup Temperature 293 °KElectronic Gain 86 dBMax Gain Ripple (Small Scale) 10 dBMax Gain Variation (Large Scale) 3 dBNominal Noise Power 0 WNominal Schottky Power 2 WNominal Total Power 2 WMaximum (Saturated) Power 50 WKickersBeta Function @ Kicker 35 mNumber of Kickers 32Kicker Impedance 100 ΩKicker Gap 30 mmKicker Width 22.5 mmKicker Sensitivity 0.62Kicker Loss(2 GHz) 2 dBKicker Loss(4 GHz) 2 dBNumber of Kicker Tanks 1Overall Tank Length 1.84 m


3. Technical Components

In this section the specific technical scope of the Recycler upgrade of the MainInjector project is described. For each category of components technical specificationsand counts are reviewed.

3.1. Magnets (WBS 3.1.1)

Except for a small number of dipole and quadrupole correction magnets, all magnetsin the Recycler ring and its associated injection and extraction beamlines are of thepermanent variety. In this section the shape, weight, placement, strength, and tolerancesof the magnets are described.

3.1.1. Recycler Ring Overview

In the Recycler ring there are 9 unique major magnet types, all of which arepermanent magnets. Table 3.1.1 contains name definitions for the magnet types. Thetwo magnet categories which make up the majority of the magnets are gradient dipolesand pure quadrupoles. Figure 3.1.1 and 3.1.2 contains engineering cross-sectionaldrawings of these two categories.

Table 3.1.1: The definition of names representing magnet types.

Type Name Description

1 RGF Focusing Gradient Dipole in a Normal Bend Cell2 RGD Defocusing Gradient Dipole in a Normal Bend Cell3 RGS Gradient Dipole in a Dispersion Suppression Cell4 RQM Straight Section Quadrupole5 RQS(1-8) MI-60 Trim Quadrupoles6 RQPT(0-4) MI-60 Phase Trombone Quadrupoles7 RLA Lambertsons at the Ends of Transfer Lines8 RMG Mirror Gradient Dipole near MI-30 Recycler Lambertsons9 RVD Vertical Dipoles for Transfer Lines

The number of gradient magnets in the ring, along with the design multipole strengthsand lengths, are listed for each type of gradient magnet in table 3.1.2. Note that only thenormal cell magnets in the region of nominal dispersion contain a sextupole componentof the magnetic field in order to combat the natural chromaticity of the uncorrectedlattice. It turns out that the present version of the Recycler lattice, version 10, has equalgradient and bend in the focusing and defocusing dispersion suppression gradientmagnets. Therefore there are only three pole piece shapes in all of the gradient magnetsin the Recycler ring.


Figure 3.1.1: Gradient magnet profile. These magnets are composed ofdouble bricks on top and bottom.

Figure 3.1.2: Quadrupole magnet profile. These magnets are composed oftwin cut bricks behind each pole.


The same information for the main quadrupoles in the ring is displayed in table 3.1.3.Note that the focusing and defocusing quadrupoles are identical except for a 90° rotation(or brick polarity reversal during fabrication).

Table 3.1.2: Number, magnetic lengths, and magnetic multipoles ofgradient magnets in the Recycler ring. The dispersion suppressionfocusing and defocusing magnets are now identical. Therefore, there areonly three different shape gradient magnet pole pieces in the entire ring.

Name Length (m) Number Bo (kG) B1 (kG/m) B2 (kG/m2)

RGF 4.267 108 1.4494 3.515 3.566RGD 4.267 108 1.4494 -3.365 -5.997RGS 2.845 128 1.4494 7.877 0

Table 3.1.3: Number, lengths, and magnetic multipoles of quadrupolemagnets in the Recycler ring. Note that only one pole shape is required inorder to produce all of the magnets.


RQM (F) 0.5 28 0 26.816 0RQM (D) 0.5 28 0 -25.640 0

Table 3.1.4: List of the vernier quadrupoles needed on either side of theMI-60 straight section to correct the lattice function distortions caused bythe horizontal bypass of the Recycler around the Main Injector RF cavitypower tubes.


RQS1 0.5 2 0 6.041 0RQS2 0.5 2 0 -10.232 0RQS3 0.5 2 0 -12.926 0RQS4 0.5 2 0 19.763 0RQS5 0.5 2 0 -7.001 0RQS6 0.5 2 0 -4.235 0RQS7 0.5 2 0 -9.580 0RQS8 0.5 2 0 4.291 0

At MI-60 the straight section is empty of specialty components except for the four RFcavities. Because of the cost of a distributed quadrupole circuit for betatron tune controlof the Recycler, it has been decided to employ the phase trombone method of tunecontrol. By adjusting 5 families of quadrupoles in the MI-60 straight section, the phaseadvances in the horizontal and vertical planes are independently adjustable whilesimultaneously maintaining the same Twiss parameter values at the ends. By keeping theend Twiss parameters constant, no lattice mismatches result and the straight sectionactually appears as a phase trombone. In table 3.1.5 the different settings of the phase


trombone quadrupoles are displayed. While holding the maximum beta function in thestraight section to under 200 m, a tune range of ±0.5 tune units in either plane can berealized. This maximum beta function value represents an almost doubling of the beamsize. A 3" diameter round beam tube will be used in the MI-60 straight section topreserve the admittance of the entire ring.

The initial implementation of these quadrupoles, as well as the two skew quadrupolesrequired to cancel coupling globally, will be electromagnets - trim quadrupoles reusedfrom the Main Ring and powered by reused Main Ring trim power supplies. A possiblelater improvement would be to replace the electromagnets with a system to roll adjacentpermanent magnet quadrupoles in a counter-phased manner using stepping motors. Thiswould enhance the the high reliability mission of the Recycler. Lattice calculations showthat in the rolling scheme three short magnets are required to implement each variablestrength quadrupole, but these magnets can also serve as the skew quadrupole correction.

To adjust the beam position and angle through the Lambertson magnets duringinjection and extraction, and to permit aperture scans, we will install both horizontal andvertical four-bumps at each Lambertson in the Recycler, a total of 24 magnets. Thesewill be reused Main Ring trim dipoles powered by Main Ring trim power supplies. At8 GeV the Main Ring trims are sufficiently strong, even shimmed to a larger aperture.

Table 3.1.5: Phase trombone quadrupole strengths at MI-60 in a lattice inwhich the standard phase advance per cell in each transverse plane ismaintained.


RQPT0 0.5 2 0 -36.676 0RQPT1 0.5 4 0 32.033 0RQPT2 0.5 4 0 -34.601 0RQPT3 0.5 4 0 32.679 0RQPT4 0.5 2 0 -32.827 0

3.1.2. Transfer Line Overview

There are also a significant number of permanent magnets employed in the threetransfer lines associated with the Recycler. The two transfer lines between the MainInjector and the Recycler at MI-30 have the largest number of magnets associated withthem, since the transfer occurs over a segment of the tunnel which is bending.Table 3.1.6 contains a summary of the permanent magnets envisioned for both lines. Themirror gradient magnets are required in the Recycler and the beam line at the first(otherwise) normal defocusing gradient dipole downstream (upstream) of theLambertson. The problem is that the transfer is taking place in a normal arc cell, and thedistance between the Lambertson and the first permanent magnet gradient magnet is toosmall to have both a ring and matching beamline gradient magnet stacked on top of oneanother. Since the mirror dipoles can be constructed such that there is only 0.75" of fluxreturn for each magnet between the ring and transfer line beam pipes, the minimumseparation of 4.5" at the leading edge of the magnets can be accommodated.


Table 3.1.6: Total number of magnets of each type required in bothtransfer lines at MI-30 between the Main Injector and the Recycler.


RLA 4.064 4 1.5232 0 0RVD 4.267 4 1.4494 0 0RMG 4.267 4 1.4494 -3.365 -5.997

RQM (F) 0.5 4 0 26.816 0RQM (D) 0.5 2 0 -25.640 0

RGS 2.845 8 1.4494 7.877 0

The transfer lines and the abort line all require vertical bends beyond that provided bythe Lambertson magnets. The strength, length, and aperture of these magnets match thenormal gradients in the ring. Therefore the plan is to copy the design, substituting a newpole shape to produce a dipole field.

In the proton abort line three 20 mrad permanent magnet dipoles and two quadrupolesare necessary. In addition, a mirror dipole or permanent magnet Lambertson is alsoneeded. These counts are summarized in table 3.1.7.

Table 3.1.7: Total number of magnets of each type required in theRecycler abort line.


RQM 0.5 4 0 26.816 0RLA 4.064 2 1.5232 0 0RVD 4.267 3 1.4494 0 0

3.1.3 Permanent Magnet Design Features

The basic design of the permanent magnet dipole is shown in figure 3.1.3. It is a1.5 kG gradient (combined-function) dipole with a 2 in. gap at the center, a 5.5 in.horizontal aperture and a 3.5 in. horizontal good-field aperture. Overall dimensions are9.5 in. high by 11.5 in. wide by approximately 13 ft. long. The weight is typically2000 lb. The magnets are straight and the sagitta of the beam inside a magnet is typically1 cm. The beam pipe dimensions under vacuum are approximately 1.75 in. vertically and3.75 in. horizontally. The precise parameter values for each of the individual gradientmagnet types appear in table 3.1.8.

The design is a so-called “hybrid” permanent magnet in which the field is driven bypermanent magnet material and the field shape is determined mainly by steel pole pieces.The field quality, which is shown in figure 3.1.4, is designed to give a vertical magneticfield error of less than 1x10-4 across the designated good field region. The permanentmagnet bricks drive flux into (from) the pole tips from the top (bottom) (see figure 3.1.5).The entire assembly is enclosed in a flux return shell 0.75” thick. Solid "bar stock"components are used throughout rather than laminations. The pole tip steel is 1008 low


carbon steel and the flux return is construction grade (A36) steel. The design fieldharmonics which correspond to the design shape shown in figure 3.1.4 are listed in table3.1.9.

Figure 3.1.3: Permanent magnet gradient dipole components shown in anexploded view. For every 4" wide brick there is an 0.5" interval oftemperaature compensator material composed of 10 strips.


Table 3.1.8: Design and physical parameters of Recycler focusing (RGF),defocusing (RGD), and dispersion suppresser (RGS) gradient magnets.

Parameter RGF RGD RGSMagnet Width (in.) 11.5 11.5 11.5Magnet Height (in.) 9.0 9.0 9.0Physical Length (in.) 175.0 175.0 119.0Total Weight (lb.) 2691 2691 1800Magnetic Length (in.) 168.0 168.0 112.0Bend Angle (mrad) 21 21 14Beam Sagitta (mm) 10 10 5Flux Return Weight (lb.) 1496 1496 1017Pole Tip Weight (lb.) 302 302 202Ferrite Brick Weight (lb.) 710 710 461Compensator Weight (lb.) 133 133 86Aluminum Weight (lb.) 50 50 34

Table 3.1.9: Calculated magnetic field harmonics for the Recycler arc cellfocusing gradient magnet pole shape design.

N Normal Skew N Normal Skew

1 10000 -0.07 7 0.02 -0.022 610.03 0 8 0 0.013 15.21 -0.06 9 0.04 0.014 -0.11 0 10 0.01 -0.025 -0.1 -0.02 11 -0.07 0.016 0.01 -0.01

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

-1.5 -1 -0.5 0 0.5 1 1.5

Horizontal Position (inch)

Fiel

d E

rror

∆B

/Bo

(x10

,000

)

Figure 3.1.4: Design magnetic field imperfection across the horizontalaperture of a Recycler gradient magnet. Generated by Poisson, the ripplein the field is due to the finite extent of the poles and the trapezoidalapproximation of the pole shape.


As shown in figure 3.1.6, the end fields of the magnets are terminated by fluxclamp/end plate assemblies which are magnetically connected to the flux return shell.These plates prevent the stray flux from leaking out and saturating the mu-metal/soft ironshielding of the beam pipe between magnets. The end plates are removable to allowaccess to the ends of the pole tips for field quality shimming operations.

Figure 3.1.5: POISSON field map of a Recycler gradient dipole.

stainless steel Beam Pipe

Mu-MetalSoft Iron

Flux Return

Strontium Ferrite Bricks

TemperatureCompensator

Strips

Flux Clamp/ End Plate

Field QualityPole Shim

Region

FieldStrengthShim Region

PoleTip

Figure 3.1.6: Side view of magnet, showing transition from magneticshielding of naked beam pipe to magnet flux return. Also indicated are theregions at the ends of the pole tips devoted to shimming the field shape,and the ends of the ferrite bricks which are used to trim the strength of themagnet by adjusting the total amount of magnetic material.


3.1.4. Permanent Magnet Material

We have chosen Type 8 Strontium Ferrite (Type 8 Strontium Ferrite data sheets &specifications from Arnold, Crucible, and Hitachi) as the permanent magnet materialbecause of its low cost and high stability over time, temperature, and radiation.Strontium ferrite is the material of choice in automotive applications and is available atlow cost in standard grades and sizes from multiple vendors. It has documented stabilityin applications such as NMR magnets and is commonly used in ion pumps in acceleratorapplications. Materials from the three major U.S. vendors were evaluated and performedwell in the R&D program.

3.1.5. Magnetization and Strength Trimming

Ferrite bricks are shipped unmagnetized from the foundry and are magnetizedimmediately prior to assembly using a 2 Tesla dipole. The bricks are individuallymeasured and assembled into “kits” each containing a specified total magnetic strength ofbrick. The magnet design is such that a magnet fully loaded with bricks of nominalstrength is 3~5% stronger than required. Dummy bricks, fractional bricks and spacers areused to control the total strength of the “kits” to correct for brick-to-brick and lot-to-lotvariations. A final strength trim is accomplished by adjusting the amount of ferrite at theends of the magnet.

3.1.6. Temperature Compensation

The intrinsic temperature coefficient of the Ferrite material (-0.2%/°C) is canceled[Dallas 1995 PAC papers on permanent magnets by Bertsche & Ostiguy, Foster &Jackson] by interspersing a “compensator alloy" (Carpenter Technologies Compensator30 type 4 data sheets from Telcon data sheet, Eagle Alloys, Sumitomo Heavy metals)between the ferrite bricks above and below the pole tips. The compensator is an iron-nickel alloy with a low Curie temperature and therefore a permeability which dependsstrongly on temperature. This shunts away flux in a temperature dependent mannerwhich can be arranged to null out the temperature dependence of the ferrite. We find thatthe degree of temperature compensation is linearly related to the amount of compensatormaterial in the magnet. Thus the degree of compensation can be “fine tuned” to therequired accuracy by adjusting the amount of compensator at the ends of the magnet in amanner similar to the strength trimming with the ferrite. For example, a 20-foldreduction of the temperature coefficient (from 0.2%/°C to 0.01%/°C) requires that theamount of compensator in the magnet be adjusted correctly to 1 part in 20. This poses nodifficulties for production.

The range and accuracy of the required temperature compensation is determined bythe expected variation in tunnel temperature. Data from the Main Ring tunnel during atypical period of operations can act as a guide to predict Main Injector tunneltemperatures. Figure 3.1.7 contains data from a Main Ring sector which had themaximum temperature variation during the time plotted. Note that a ±1°C temperaturevariation is a pessimistic estimate.


Days

Mai

n R

ing

Tun

nel T

emp.

(°C

)

29

30

31

0 2 4 6 8 10 12 14 16

Figure 3.1.7: Measured Main Ring tunnel temperature during a typicalperiod of operations. Note that on the second day the Main Ring wasturned off for a few hour access.

The ultimate limit to the temperature range of the compensation technique is set bythe nonlinearities of the opposing temperature coefficients. The ferrite material appearsto be highly linear over the relevant temperature range. However, the compensatormaterial tends to become weaker as it approaches its effective Curie temperature ofapproximately 55°C. Figure 3.1.8 indicates the degree of compensation achieved on atest magnet using ferrite and compensator materials from the 8 GeV line production (lowbidder) vendors. Note that the maximum deviation is ±1x10-4 over the range 31± 7 °C.

Temperature (°C)

0.995

0.99550.996

0.9965

0.9970.9975

0.9980.99850.999

0.99951

1.00051.001

1.00151.002

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Uncompensated-0.2%/°C

Compensated

Mag

net S

tren

gth

(Nor

mal

ized

to 2

5 °C

)

Figure 3.1.8: Field strength vs. temperature for a stability test magnetusing pre-production samples from the selected vendors for compensatoralloy and ferrite.


3.1.7. Magnet Assembly

The assembly sequence is as follows (see figure 3.1.3). The pole pieces are pinnedand bolted to the aluminum U channel side members hold them in place to make a boxstructure. The bricks are placed on the back of the pole pieces, interleaved with the stripsof compensator. The magnetic forces hold them in place. The top and bottom flux returnplates are lowered onto the assembly using meachanical fixturing to control the operationin the presence of strong magnetic forces. The side flux returns are then moved to theirplaces using the fixturing and bolted to the top and bottom plates. The steel end platesare installed and bolted to the flux return.

After the initial assembly each magnet's field strength and shape will be measured atthe assembly facility. On the basis of this shape measurement, the steel shim piecesdescribed below will be machined to trim the field shape as needed. In parallel themagnet will be placed in a large freezer and cooled to 0 degrees C to stabilize it againstfurther temperature excursions (see section 3.1.9 Stabiliy Issues) during installation. Onremoving the magnet from the freezer the temperature and strength will be measuredimmediately. Assuming that the magnet is correctly compensated, the strength trimmingcan be determined from this measurement. After the magnet warms to room temperature,the strength will be remeasured to verify that it is correctly compensated, then the endshims will be installed and the appropriate bricks added or removed to trim the strength.A final measurement will confirm that the correction was successful and document thefinal configuration.

3.1.8. Field Quality

The field quality of the Recycler magnets must be adequate for a storage ring, i.e.roughly ∆B/B = ±0.01% over a good-field aperture chosen to be 1.75 in. horizontal by3.5 in. vertical, or ±0.02% over ±25 mm in the performance simulations. The basicmanufacturing strategy is to maintain construction tolerances of a few times 0.001 in. forthe iron pole tips of the magnets, which is sufficient to achieve roughly 0.1% field defectover the aperture. The field shape is then trimmed to an accuracy of 0.01% usingadditional metal pieces on the ends of the magnet pole tips. This procedure isconsiderably simplified since only the integrated field is of interest, and the shims onlyhave to work at a single level of excitation (no saturation effects).

3.1.9. Stability Issues

In order to address the issue of long-term stability of strontium ferrite, 10 test dipoles"stability test magnets" were built and subjected to a variety of environmental conditionswhich could possibly have an impact on the magnetic stability. The effects studiedincluded varying the ferrite and compensator suppliers (most of the stability magnetswere built with Hitachi bricks and Carpenter type-4 compensator), heating and coolingeffects, radiation, partial demagnetization of the bricks, and simple aging.

One effect which has so far been demonstrated to have an immediate and irreversibleeffect on the magnet strength is cooling below 0°C. A magnet was cooled from roomtemperature (20°C) to 10°C, and no decrease in strength was seen when warmed back upto room temperature. However, on freezing to 0°C, the magnet lost 0.05% of its original


strength on warm-up. It was then cooled to -20 C, and it lost 0.1% of its original strength.This magnetization loss appears to be a one-time effect, provided one does not cool themagnet below the previous coldest temperature it has experienced. Thus, the magnet wascooled a second time to -20 C, and did not suffer any additional degradation in strength.This effect has been observed on two different magnets.

Time (days)

Mag

netic

Fie

ld (

Gau

ss)

1450.0

1450.2

1450.4

1450.6

1450.8

1451.0

1451.2

1451.4

1451.6

0.01 0.1 1 10 100 1000

Figure 3.1.9: Field strength vs. time of a stability test magnet. Over 4decades the data follows an expected log-time dependence. The linerepresents a log-time decay rate of 2.2x10-4/decade.

Time (days)

Mag

netic

Fie

ld (

Gau

ss)

1401.11401.21401.31401.41401.51401.61401.71401.81401.91402.01402.1

0.1 1 10 100 1000

Figure 3.1.10: Field strength vs. time of a stability test magnet. Thismagnet was composed of bricks which were demagnetized by 5% beforeassembly. The line represents a log-time decay rate of 2.4x10-4/decade.


Some magnets were monitored for aging by measuring their strength (at the midpointof the aperture, using an NMR probe) as a function of time since production. The data,shown for two magnets in figures 3.1.9 and 3.1.10, is consistent with an expected log-time aging [Kronenberg & Bohlmann, J. Appl. Phys. 31, 82S (1960); Street & Wooley,Proc. Phys. Soc. A62, 562 (1949)], and the present upper limit on aging derived from thisdata (2.5x10-4/decade) corresponds to less than 0.05% of field change over a 20-year lifespan for the magnets. Aging at this level can be easily accommodated by changing theenergy of the Booster, Main Injector, Debuncher, and Accumulator rings to match thecentral energy of the Recycler.

One magnet was irradiated by a source putting out approximately 0.8 Mrad/hour for268 hours. Taking into account down time, the net average flux to the magnet was about0.3 Mrad/hour for about 100 Mrads. The observed change in magnet field isapproximately 0.5 Gauss out of 1465 Gauss, or ~3x10-4 which is within the range ofallowed variation. No change was seen in a series of low level initial doses. In addition,mechanical disturbance such as dropping the magnet had no measurable effect above0.3 Gauss.

One concern voiced in some project reviews was the potential for strengthdemagnetization of the Recycler permanent magnets due to the A.C. component of thestray fields in the tunnel from Main Injector components. A 1 m long prototype of an arccell focusing gradient magnet was exposed to 100 magnetic field ramps generated by aHelmholtz coil. With an estimated field in excess of 10 Gauss, no observable field loss(to an accuracy of 1x10-5) was observed.

Another review concern was changing of the field magnitude or shape from the150°C in-situ bake of the vacuum system. ANSYS calculations of the bake procedurepredict that the permanent magnet bricks never exceed 40°C due to thermal insulationaround the beam pipe and heat transport through the aluminum and steel components outto the air. In order to verify theoretical predictions that this temperature is not harmful tothe magnetic field of gradient magnets, the 1 m long prototype magnet was heated to auniform temperature of 60°C. No field strength or quality changes were observed.

3.1.10. Magnet Measurement Requirements

A rotating coil probe has been built for measuring all of the dipole and gradientmagnets for the 8 GeV and Recycler projects. This probe is a Morgan-style probe,having windings sensitive to dipole through 14-pole. It is 16 feet in length, which allowsmeasurements of integrated strength of all the anticipated magnets. Morgan probes havethe advantage of cleanly separating dipole, quadrupole, and higher-order harmonics, anessential feature for measuring gradient magnets. The probe has been tested on the twopre-production magnets, and has demonstrated the ability to meet the specifiedrequirements of measuring the integrated strength to better than 2x10-4 and the harmonicsto about 0.2 units (0.2 parts in 10,000 at 1 in.). An additional probe with a tangentialwinding geometry is being considered to improve the sensitivity to higher magnetic fieldmultipoles.

A redundant measurement system will use a single stretched wire to scan thehorizontal aperture. This device will provide a second measurement of the strength, butwill also map the field shape in a region inaccessible to the Morgan coil (beyond


|x|>0.8 in.). This stretched wire system has been in use in measuring Main Injectorquadrupoles.

A Hall probe measurement system to measure the central field as a function of thelongitudinal position will be necessary. A similar system is used in the Main Injectordipoles. The field strength profile of the magnet as a function of distance inside themagnet must be generated with sufficient resolution to determine the bend center toapproximately 0.5".

3.1.11. Field Shape Tuning

Using the two full length gradient magnets already produced for the 8 GeV lineproject, studies have been performed attempting to identify an algorithm for tuning thefield harmonics to a level required by lattice and beam stability criterion. Because thesemagnets do not change in field, end packs shaped to eliminate unwanted field harmonicamplitudes are relatively simple to employ. Tests show that field deviations across theaperture as large a 0.1% can be corrected.

We now have experience with constructing identical models of full length Recyclergradient magnets. Figure 3.1.11 shows the multipole difference between two magnetsbuilt identically. Repeated measurements were performed on each magnet, and thedifference RMS is shown to give one a feeling of the expected error bars on thesemeasurements. The dominant error is in the normal gradient, which is easily tuned withend shims discussed in the next paragraph. The skew multipole differences are generatedby a pole potential imbalance caused by unequal brick strengths behind the top andbottom poles (before equalization was carried out). In experiments with equalization thetransfer function between brick strength and skew multipole strength has been measured.The results of these measurements scaled to the observed difference in these two magnetsare also displayed. The dominant source of skew moment is this easily correctable polepotential imbalance.

As shown in figure 3.1.12, the shimming is presently accomplished by adding extrasections of gradient poles which are shaped longitudinally in order to generate therequired multipole correction. These shapes are generated by measuring the fielddeviation in each magnet, using the measurement program to generate an input file for acomputer controlled wire EDM machine, cutting a piece of normal pole piece, and thenmounting the extra pole pieces (one top and one bottom) on one side of the magnet. Thelower the multipole moment, the bigger a multipole correction can be made for a givenaverage shim thickness. As can be seen in figure 3.1.11, the higher the multipole momentthe smaller the multipole error which can be generated with expected fabricationimperfections.


0

0.5

1

1.5

2

2.5

N2

N3

N4

N5

N6

N7

S2

S3

S4

S5

S6

S7

Field Harmonic (Normal and Skew)

Fiel

d H

arm

onic

Dif

fere

nce

(∆

B/B

@ 1

" x1

0,00

0)

Brick RemovalDifference AverageDifference RMS

Figure 3.1.11: Difference in magnet field quality due to difference inmagnet fabrication measured on two identical full length Recyclerprototype gradient magnets.

FluxReturns

MagnetPoles

End Flux Clamps

PerfectMagnet

QuadrupoleCorrection

SextupoleCorrection

OctupoleCorrection

Figure 3.1.12: Sketch of the scheme used to correct any measured fieldshape errors. Using these prototype shapes and linear superposition, avery good correction algorithm has been generated and measured.

3.1.12. Recycler Magnet Key Performance Specifications

The table below contains the basic key specifications for the Recycler permanentmagnets. These are discussed, justified, and quantified at exhaustive length inMI-Note #150. Many of the values listed in this table, such as the design lifetime, arerather arbitrary and are intended to guide engineers and technicians toward an appropriatelevel of care and ruggedness.


Table 3.1.10: Miscellaneous magnet performance specifications. Many ofthe specifications are quite far from anticipated parameter values and donot present concerns.

Design Lifetime 30 yearsOperating Temperature 20°C (68°F) to 35°C (95°F)Storage Temperature 5°C (41°F) to 50°C (120°F).Humidity 0%-100%Corrosion Resistance All parts resistant, plated, or painted.Bakeout Compatibility Beam Pipe @ 150°C, Magnet @50°CTemperature Stability of Field Strength ±0.05% full spread over 10-35°CTemperature Stability of Field Shape < ±1 unit in any multipole for ±10°CTime Stability ∆B/B < 0.05%/yr.Radiation Resistance ∆B/B < 1% for 1E9 RadsShock & Vibration ∆B/B < 0.1% from normal handlingRadiation Activation Comparable to steel/copper magnetsGood-Field Aperture ±1.25” at δ By/B0 <1E-4Dipole Vertical Aperture 2.0” between the pole tips (at X=0)Quadrupole Pole Tip Radius 1.643” (XY = 1.350 in2,, same as MI)Magnet Sagitta Zero (straight magnets)Beam Sagitta Inside Dipole ~1cmField Uniformity in Z ±5% (random) or betterBend Center uncertainty ±1cm in Z (measured and surveyed)Field Strength Modification possible in range [+3%,-5%].Field Shape Modification +/- 10 units (modify end shims)Magnetic Field in Flux Return <1 TeslaMagnetic Shielding of Beam Pipe 2-layer (µ-metal + iron foil)Termination of End Fields via Flux Clamp / End Plate of MagnetsEnd Fields < 5 Gauss 2.5 cm past end of magnetBeam Pipe Fixturing allows ±1cm horiz. range of motionSurvey Fiducials 8 “nests” at corners of magnetMechanical Rigidity (sag) < 0.020” for 25% , 75% support points

3.1.13. Permanent Magnet Quadrupoles

One type of permanent quadrupole is required for the Recycler. The standard designhas the same 1.643” pole tip radius as the Main Ring/Main Injector quadrupoles. AllRecycler quadrupoles are 0.5 m long. Different strengths are implemented with differentbrick concentrations and flux shorting shims.

The quadrupoles have a hybrid design analogous to the gradient dipole. The fieldshaping is provided by machined steel pole tips and the field is driven by strontium ferritebricks. The version which is currently under fabrication for the 8 GeV line and RecyclerR&D is shown in figure 3.1.13. Temperature compensation of the ferrite is provided by


interspersing strips of compensator alloy between the bricks along the length of themagnets. The overall strength of the magnet is trimmed by adjusting the amount ofpermanent magnet material behind each pole tip, and the field shape is trimmed byadding steel shims to the ends of the pole tips. A steel flux return shell surrounds themagnet, and “flux clamp” end plates are used to terminate the field at the ends of themagnet.

Fe

Alum

Alum

Alum AlumFe

Fe

Fe

Ferrite

Ferrite Ferrite

Ferrite

Ferrite Ferrite

Ferrite Ferrite

Fe Fe

FeFe

Figure 3.1.13: Cross-section of a rectangular quadrupole magnet.

3.1.14. Permanent Magnet Lambertsons

Transfer lines to and from the Recycler and 8 GeV line require a total of sixLambertson magnets. A standard design (2 kG, 3m long) has been adopted whichprovides a 21 mrad bend for the 8.9 GeV/c extracted or injected beam. In the typical


application the circulating beam is in the field-free region and is kicked horizontallyoutwards into the bend region where it is deflected upwards or downwards.

CirculatingBeam

ExtractedBeam

Base Plate for

Pole Tip Assembly( Follows Extracted Beam )

Field-Free Region

Figure 3.1.14: Side view of a Lambertson magnet showing the stored andextracted beam trajectories, and the slant in the extraction channel tominimize sagitta effects.

circulating protons

transferred beams

RLA RLB

RLC RLD

circulating protons

Figure 3.1.15: Lambertson construction geometries required to service allof the beam transfer needs of the Recycler.

To minimize sagitta and economize on magnet aperture, the pole tip assembly for thebend region follows (to first order) the trajectory of the deflected beam. The pole tip istherefore not parallel to the field-free trajectory, but is offset and canted by 1/2 of thebend angle or approximately 10 mrad. See fig. below. This is easily accomplished sincethe cutout of the field free region is machined out of the solid plates used to piecetogether the “base plate” of the Lambertson. See figure 3.1.14 for a sketch of theLambertson geometry.

Two polarities of permanent-magnet Lambertsons are required: one which deflectscounterclockwise protons (and clockwise antiprotons) downwards, and one whichdeflects them upwards. For each polarity there are two possible orientations of the “base


plate” containing the field-free cutout: one which deflects incoming beam from the left,and another from the right. Figure 3.1.15 summarizes these options.

Two successful prototype permanent Lambertsons (2.2 kG and 3.55 kG, each 1mlong) have been produced and tested. The bend field uniformity was adequate and theaverage field in the “field-free” region was <0.5 Gauss. The cross-sectional view of thepermanent Lambertson is shown in figure 3.1.16.

Figure 3.1.16: Permanent Lambertson magnet cross-section withPOISSON field map superimposed. The field free circular region is thecirculating beam aperture. The horizontal field in the extracted beam linesteers the beam up or down. Three bricks drive flux into the central solidpole piece, one from the back and one from each side (top and bottom inthe figure).

3.1.16: Magnet Hangers and Installation

The hangers and installation for the Recycler are presently being modeled within thepermanent magnet 8 GeV line project. It is expected that the magnets will be cheaper andeasier to install than their Main Injector counterparts. For instance, each gradient dipoleweighs approximately 1 ton, as compared to 20 tons in the Main Injector. The cross-section of the magnets are much smaller, and the magnets are shorter. The quadrupolesare expected to weigh approximately 200 lbs. each.

In most locations around the ring it is expected that the hangers will be bolted to theunistrut sections welded to the iron bars captured in the concrete tunnel walls. In a fewlocations where the tunnel shape changes or where Main Injector transfer lines to theBooster, Accumulator, and Tevatron exist, it will be necessary to build some moreelaborate hangers.


3.2. Vacuum (WBS 3.1.2)

There are 104 cells in the Recycler ring. Because of the low outgassing ratesaccessible with the hydrogen degassing technique described in chapter 2, a vacuumpressure two orders of magnitude lower than the Main Injector can be achieved with thesame number of pumps. In this discussion the type, placement, and processing ofRecycler ring vacuum components are reviewed.

3.2.1. Geometry Overview

In the Main Injector there are 6 ion pumps per cell and the length of vacuum sectors isapproximately 500' (150 m). In the Recycler there will be one ion pump per cell, for atotal of 104 ion pumps. Between the ion pumps there will be 5 titanium sublimationpumps (TSPs) per cell to achieve an average of pressure of approximately 1x10-10 Torr.The benefit of TSPs are lower cost and lower ultimate pressures. Since the length ofnormal cells is 34 m and the length of dispersion cells is 26 m, the longest vacuum sectorpossible if the isolation valves are spaced every 8 cells apart is 270 m. Therefore, thetotal number of sector valves is 104 ÷ 8 = 26. Figures 3.2.1 through 3.2.3 containsketches of the vacuum system in normal arc cells, straight section cells, and dispersionsuppression arc cells.

34.6 m

F D D F F

TSP

IP IPH V

TSP TSP TSP TSP

H V

5.75 m 5.75 m

F

TSP TSP

Figure 3.2.1: Sketch of the vacuum system in a normal arc cell. Thehorizontal (H) and vertical (V) beam position monitors have attached tothem titanium sublimation pumps (TSP) in order to maintain a lowaverage pressure and to minimize the number of welds in the tunnel.

F D D F FF

TSP

IP

34.6 m

H V

TSP TSP TSP TSP

H V

5.75 m 5.75 m

IP

TSPTSP

Figure 3.2.2: Sketch of the vacuum system in a normal straight sectioncell. Except for the fact that the quadrupoles are much shorter than thegradient magnets in the normal arc cell, nothing is different with respect tofigure 3.2.1.


4.25 m

F D D F FF

TSP

IPH

TSP

V

TSP TSP

H

TSP

V

4.5 m

25.9 m

IP

TSP TSP

Figure 3.2.3: Sketch of the vacuum system in a dispersion suppresser cell.

With the exception of the MI-60 phase trombone straight cells which need additionalvertical aperture and hence a round 3" O.D. beam tube, the Recycler vacuum tube is a1.75" inside height by 3.75" inside width ellipse. It is produced by crushing a standard 3"O.D. beam tube with a wall thickness of 0.065".

3.2.2. Beam Position Monitor Assemblies

In order to minimize the cost of the vacuum system, it is necessary to minimize thenumber of welds in the tunnel. This means generating as many pre-fabricated assembliesin industry and staging areas as possible. In addition, if possible it is good to mergemultiple functionalities into the same component. For instance, the beam positionmonitor (BPM) can also act as an ion clearing electrode. Another possibility which willdepend on further surface physics research by personnel at FNAL, LBNL, and KEK is theuse of titanium electrodes in order to get ion pumping from the BPM electrodes.

Because both protons and antiprotons are injected into the Recycler for operations,commissioning, and studies, the beam position monitors need to be bi-directional.Capacitive split-tube electrodes are optimum in a geometry where the transverse beamsize is comparable to the electrode dimensions. Capacitive electrodes are also perfect forthe creation of ion clearing electrodes. In order to minimize the impedance effects of theBPMs, the electrodes are shaped to match the vacuum chamber, the outer wall of theBPM is the same shape as the electrodes and only large enough to stand off the 700 V ofion clearing voltage. For the same reasons, the gaps between the electrodes and thevacuum chamber wall are as small as possible without compromising the capacitance(and hence sensitivity) of the electrodes.

As can bee seen in figures 3.2.1 through 3.2.3, in every Recycler half cell there arealways two BPMs separated by a straight, unoccupied section of vacuum pipe. At eachof these BPM locations a bellow is required to absorb the length increase which occurs inthe vacuum system when it is insitu baked at 150°C. In order to simply the beam pipepositioning stands and installation, the bellows are always located to the outside of bothBPMs. As shown in figure 3.2.4, between the BPMs and bellows are TSPs. The TSPport is a rectangular slot 4" long and 1" high centered on the horizontal edge of thechamber (see figure 3.2.5). The horizontal edge of the vacuum chamber supports theminimum of the image current distribution, so therefore this geometry has the lowestimpedance impact while simultaneously maximizing the conductance to the pump itself.


1 3/4"

12"

12 1/2"

2 3/4"

23 1/2"

3"6"

ShieldedBellow

TitaniumSublimation

Pump

Beam Position Monitor /

Ion Sweeping Electrodes

4"

4"

2 3/4"3 3/4" 4"

ElevationView

PlanView

12"

Figure 3.2.4: Elevation and plan views of the BPM assemblies which eachinclude a TSP and shielded bellows. A vertical BPM is shown, which ison the downstream side of each half cell. The horizontal BPM, which isplaced on the upstream side of each half cell, has a horizontally sensitiveelectrode and the entire assembly is rotated left for right.

1 3/4"

3 3/4"

BeamChamber

6"TitaniumFilament

SulimationMoleculeBaffle

TSP

Figure 3.2.5: Beam's eye cross-section view of the TSP and its connectionto the beam tube.


3.2.3: Hydrogen Degassing Oven

Before the hydrogen degassing is performed, the tubing is washed and cleanedinternally with solvents. The tubing is then sent over to a former superconducting coilcollar hydraulic press used for crushing the pipe into the correct elliptical shape. Thedesign profile has an inner full height of 1.75 in. and a full width of 3.75 in.

In order to achieve this vacuum system configuration and achieve an average vacuumof approximately 1x10-10 Torr, it is necessary to hydrogen degas every component. Thetest oven shown in figure 3.2.6 will be used for specialty pieces such as 1.5" diametertubing for gauges. The 3" diameter tubing used to generate the vacuum chamber itselfneeds to be processed at a rate of approximately one half cell per day in order to keep upwith the projected rate of magnet production. This criterion requires three 20' pipes perday. As shown in figure 3.2.7, by creating a new oven which has a 12" diameter, a totalof six pipes per day could be processed. Since the processing requires that the tubing stayat a temperature of 500°C for approximately 12 hours (or 900°C for 30 minutes for thosewho prefer the higher temperature approach) and the time constant of the heating andcooling is approximately 4 hours, one batch of six pipes per day is a convenientprocessing rate. This requires that a technician spend approximately 1 hour per day toempty the previous day's tubing, clean the oven, load the next batch, and then start thecontrol system computer which automatically performs the processing.

Vacuum PumpVacuum Vessel

Ground Connection

Power Connection

Ceramic Feedthroughand Expansion Bellow

Stainless Steel Pipe

Figure 3.2.6: Sketch of the test oven which will still be used to processspecialty tubing.

1

2

34

5

6

Figure 3.2.7: Profile of the crushed 3" tubing in the 12" diameterproduction oven proposed to generate an average of 2 half cells of tubingper day.


It is also necessary to hydrogen degas the tubing which makes up the beam positionmonitors, the titanium sublimation pumps, and also the shielded bellows. The split-platecapacitive pickups are created with the same 3" diameter tubing that makes up the rest ofthe vacuum system, unless the titanium electrode option is utilized. The 4.5" diametertubing which forms the vacuum wall around the pickup electrodes, the 6" diameter tubingfor the titanium sublimation pumps, and the bellows themselves are all hydrogendegassed before assembly. After the monitor, pump, and bellow has been assembledthey are again baked to 500°C in order to burn off any surface hydrocarbons from theforming and assembly of the monitor, while simultaneously hydrogen degassing all of themiscellaneous steel parts such as end plates.

3.2.4. Shielded Bellows

As shown in figure 3.2.4, associated with each BPM there is a bellow assembly. Thebellows are shielded in a manner identical to the Main Injector. The reason for so manybellows is the 150°C bakeout which is necessary for initial vacuum commissioning. Thecoefficient of elongation of stainless steel tubing is 16 µm/m-°C. A normal half cell is17 m long. Therefore, the 120°C temperature rise associated with the in-situ bake leadsto a change in length of the beam tube of 33 mm or 1.25". Given that bakes are notexpected to occur very often, a compression ratio of 2:1 is acceptable. Therefore, eachhalf cell needs at least 2.5" of uncompressed bellow. Therefore, 2" of bellow at thehorizontal BPM and 2" of bellow at the vertical BPM generate more than enoughtemperature change capacity. The other purpose of the bellows is to absorbapproximately 0.5° of bend per bellow, since the pipe segments are straight.

3.2.5. Insitu Bake System

After installation of the vacuum system it is necessary to heat it to 150°C forapproximately 24 hours in order to purge the system of water vapor. But the entire3.3 km circumference of the Recycler cannot be baked simultaneously. Instead, eachvacuum sector is baked independently. As stated earlier, each vacuum sector iscomposed of 8 cells, or 16 half-cells.

The vacuum system is heated with the use of a pair of coaxial heaters. The coaxialgeometry is used because of measurements performed on the 1 m long Recyclerprototype gradient magnet where a DC 50 Amp current caused a 16x10-4 field relativefield deviation across the magnet aperture. By using a coaxial geometry, it can beassured that no field change will occur due to leakage fields from the heater conductors.

The thermal insulation around the vacuum chamber is integrated with the magneticshielding around the chamber. As part of this system, there are 2 layers of insulation. Inaddition, the shining surface finish of the magnetic shielding also reflects back some heat.

In order for this scenario to work, a couple of conditions must be observed. First, themagnetic shielding around the beam pipe discussed in the next section must beelectrically insulated from the beam pipe. Second, in order to evenly heat the vacuumchamber it is necessary to put in flexible copper ground straps across bellows to act ascurrent bypasses. Thermal conduction through the stainless steel tubing is sufficient toheat the bellows.


Stainless SteelVacuum Chamber

In-situ BakeInsulation

Soft Iron

Mu-metal

CoaxialHeater

Figure 3.2.8: Sketch of the portable power supply connected across avacuum sector used to heat the vacuum system to 150°C.

3.2.6. Magnetic Shielding

Figure 3.2.8 contains a sketch of the magnetic shielding around the beam pipe at theedge of a permanent magnet. In order to prevent the Recycler beam from reacting to theMain Injector ramp, a hermetic magnetic seal around the Recycler vacuum chamber isrequired. In order to achieve a magnetic field reduction factor of 1000x, a layer of 4 milthick mu-metal inside a 6 mil thick layer of soft iron is employed.

Between the vacuum chamber and mu-metal, and between the mu-metal and soft iron,are layers of thermal insulation. Not only is this insulation needed for the insitu bakesystem, but it is necessary to keep the mu-metal and soft iron from coming into contact inorder to get the full magnetic field attenuation effect.

3.2.7. Beam Pipe Hangers

It is necessary to build hangers specifically for the vacuum system due to the longdistances between the magnets. The magnets themselves act as vacuum chamberhangers. In the center of the long sections between magnets the vacuum chamber hangerholds the pipe in a fixed position. During bakes the vacuum chamber lengthens towardthe bellows near the beam position monitors. The hangers connected to these monitorshave sliding joints which allow this expansion. Similarly, the pipe can slide within themagnets, but is held fixed at the end of the magnets at the 1 m short straights between themagnets. Figure 3.2.8 contains a sketch of this geometry.

Figure 3.2.8: Magnet and vacuum chamber hangers for a normal cell.Note that the magnets themselves also act as vacuum chamber stands.


3.3. Power Supplies (WBS 3.1.3)

A total of 48 dipole correctors are needed in the Recycler ring and its dedicatedtransfer lines. The power supplies for these dipole correctors are only for limited orbitcontrol around each of the 3 Lambertsons at MI-30 and MI-40 and their associatedtransfer lines. In addition, correctors are also needed at the kicker at MI-20. In order togenerate an arbitrary position and angle in each plane, 8 dipole channels are required ateach Lambertson in the Recycler. In addition, 4 horizontal and 4 vertical dipoles eachseparated by 90° of phase advance are necessary at each transfer line to adjust theposition and angle into/out of the line. See figure 3.3.1 for a sketch of the locations ofthese correctors. At 6 Amps per channel and using the Main Ring corrector magnets, adeflection of 0.5 mr is achievable. Applied near a beta function maximum ofapproximately 50 m, a closed orbit motion of 25 mm is possible. Vertically this exceedsthe 7/8" half height of the elliptical vacuum tube. The half width of the beam tube is justunder 1-7/8", so only half the horizontal aperture can be probed by the beam center.

These power supplies are already existing Main Ring "ramped corrector" controllerswhich are not going to be used in the Main Injector. The correction magnets will alsocome from the Main Ring.

L L LK K

MI

RR

MI-30MI-40 MI-20VH

VH

VH

VHVH

VHVH

VHVH

VH

VH

VH

VH

VH

VH

VH

VH

VH

VH

VH

VH

VH

L LK

VH

VH

Figure 3.3.1: Locations of the horizontal (H) and vertical (V) dipolecorrectors in relationship with the kickers (K) and Lambertsons (L)required for the Recycler ring.

The ramped corrector power supplies are also used for three other powered magnetapplications. The most important in the MI-60 phase trombone. Between each of thequadrupole pairs at MI-60 (and between the end quadrupoles and their partnereddispersion suppresser gradient magnets) a Main Ring correction quadrupole is installed.These 9 quadrupoles have enough strength to implement a phase trombone with a tuningrange of greater than ±0.1 tune units.

Also at MI-60 two skew quadrupoles from the Main Ring will be transfered to theRecycler in order to implement global decoupling tuning. Because there are 6 correctorchannels per chasis and the phase trombone only uses nine, the two skew quadrupoleswill be plugged into the spare chassis channels.

Finally, 24 Main Ring sextupoles will be installed in the Recycler and poweredindividually with ramped corrector channels. At MI-20 and MI-50 two chassis each willbe installed. In each pair of chassis 8 channels are dedicated to defocusing sextupoles


and 4 are dedicated to focusing sextupoles. In all of the above applications the 6 Ampoutput of the ramped corrector power supplies is sufficient.

3.4. RF Systems (WBS 3.1.4)

The Recycler RF system is both very simple and highly complex. Because theRecycler ring is fixed energy, coordinated control of voltage, synchronous phase, radialposition, tuning angle, cavity resonant frequency, grid bias, etc. is not necessary. On theother hand, the barrier bucket manipulations outlined in chapter 2 represent a quantumleap in phase agility and computer control.

3.4.1. High Level System

The RF cavities for the Recycler acceleration system are actually 50Ω ceramic gapswhich have sufficient inductance to pass frequencies above 10 kHz. Four of thesecavities are used to generate the needed peak voltage of 2 kV.

Connected to each of these cavities is a 5 kW amplifier and a gap monitor signalwhich feeds back into the feedback system which insures fidelity to the programmedwaveform and suppression of beam loading voltages. The amplifiers have a highpasscutoff frequency of 10 kHz and a lowpass cutoff frequency of 100 MHz. All of theamplifier feedback electronics and control electronics are in the MI-60 service building.

3.4.2. Low Level System

Most of the hardware, firmware, and software necessary for the Recycler RF systemis already being generated for the Main Injector RF system. Therefore, the estimation ofmanpower and hardware do not represent as large a level of extrapolation as might beexpected.

The system revolves around a very advanced direct digital synthesizer VME modulewhich allows computer coordinated frequency changes which are phase continuous. Byprogramming frequency ramps, arbitrary relative phases can be generated betweenneighboring synthesizers. Since all synthesizers run off of the same clock, frequencysynchronization is a digital control with no phase lock loops or feedback systemsnecessary. By sending this 52.8 MHz sinusoid through a comparator and a divide by 588counter, a turn marker can be generated which is extremely phase agile. By sending thatpulse into a module which under computer control generates a pulse of arbitrary lengthand height, the full capability of the RF system described in chapter 2 is realized.

The Direct Digital Synthesizer (DDS) VXI LLRF platform component offersperformance improvement and new implementation options for transfer synchronization.The DDS includes an AD21062 SHARC DSP, Harris Numerically Controlled Oscillators(NCO), and RF parts for SSB modulation. The DDS has three RF outputs;RF1=Asin(ωt+Φ1) , RF2=Asin(ωt+Φ2) , and RF3=Asin(ωt+Φ3). Under DSP control, theoutputs are frequency and phase agile, with controlled Φn and its first through thirdderivatives. The ωt term is determined from a 720 Hz MDAT input, filtered, andupdated at 100 kHz identically for all RF outputs. The DSP updates Φn with 16.66 kHzand 100 kHz components that include absolute and relative phase terms. Φn registers alsosum a ∆Φn term for phase control at precise rates. This specifies cogging processes


directly in the fundamental unit of interest, instead of the present cogging system's ∆Φcog= ∫∆Φ dt, taken over the cogging interval.

For the Recycler, two DDS modules are employed in parallel to generate sixindependent phase-variable waveforms which can be used to generate and manipulatebarrier buckets. Figure 3.4.1 contains a block diagram of this system. All six waveformsare created by sending the DDS channel sine waves into comparators which generatepulses at 52.8 MHz. The divide-by-588 circuit generates a single pulse each turn, whichin itself triggers an arbitrary waveform generator. All six waveforms are then summedbefore being delivered to the high level RF system.

Unlike the Main Injector, the Recycler store beams for long periods of time.Therefore, an added constraint for Recycler operations is that the phase and amplitudenoise of the pulses be very small. Measurements of the spectral purity of the output ofthe comparator are very promising.

DDS Channel 1

Divide by 588H=1

Waveform Generator 152.8 MHz

DDS Channel 6Divide by 588 Waveform Generator 6

52.8 MHz

Counter Reset Waveform and AmplitudeControl

Phase Control

S To HLRF 3 Channel VXIDDS Module 1

DDS Module 2

Figure 3.4.1: Block diagram of the Recycler low-level RF system.

3.6. Kickers (WBS 3.1.6)

The specifications for the kicker magnets needed for Recycler operations are listed intable 3.6.1. In order to keep costs low, the kicker in the Recycler ring should build on theMain Injector design experience as much as possible.

Table 3.6.1: Specifications for the Recycler magnet kickers and thetransfer kicker in the Main Injector for injection/extraction with respect tothe Recycler.

Location Direction Kick Risetime Falltime Flattop RechargeRR-20 Horz 300 G-m 1-2 µs 1-2 µs 1.6 µs 10 secMI-30 Horz 300 G-m 1-2 ns 1-2 µs 1.6 µs 10 secRR-40 Horz 300 G-m 1-2 µs 1-2 µs 1.6 µs 10 sec


A design which comfortably attains the specifications has been produced. Parts fromold Main Ring systems and the production of systems similar enough to the Main Injectorto share spare capacity have been designed. No unusual technology was invoked to reachthe above parameters.

3.7. Stochastic Cooling (WBS 3.1.7)

There are 4 stochastic cooling systems envisioned for the Recycler ring. The twotransverse systems are 2-4 GHz bandwidth betatron cooling systems. Providingmomentum cooling are a pair of systems; a 1-2 GHz and 0.5-1 GHz filter cooling system.

3.7.1. Pickup and Kicker Placement

As shown in figure 3.7.1, an amplitude modulated laser beam is used to cut achord across a potion of the ring to transmit the signals from the pickups to the kickers.The laser beams should propagate down evacuated tubes in order to prevent excessivelaser attenuation during periods of poor weather. Another benefit of laser propagationthrough an evacuated tube is the insensitivity of time-of-flight to humidity and airpressure changes.

Laser Beam Transmission

Pickups Kickers

Q213 Q1091799 nsec

1980 nsec

Antiproton Beam

Figure 3.7.1: The chord cut by the stochastic cooling systems in order tominimize the bad mixing between the pickup and kicker.

Q213VH L L L L

4 OpticalFibers to

LaserTelescope

PickupArrays

andAmplifiers

PickupArrays

andAmplifiers

Figure 3.7.2: The relative placement of the horizontal (H), vertical (V),and momentum (L) pickup tanks with respect to the magnets. Note thatthe pre-amplifiers are attached to the tanks, while the laser driver for theoptical fiber signal transmission are placed over the permanent magnets inorder to obtain some radiation shielding from Main Injector losses.


The placement of the pickup tanks around Q213 is shown in figure 3.7.2. The pre-amplifiers are attached to the pickup tanks, while the power amplifiers and optical fibertransmitters are placed over the permanent gradient magnets for radiation shieldingagainst Main Injector losses. At Q109 the relative tank placements are identical, and thefiber optic receiver and power amplifiers are again over permanent gradient magnets.The final power amplifiers, planned to be travelling wave tubes (TWTs), are attached tothe kicker tanks themselves.

3.7.2. Arrays and Tanks

The number of pickup and kicker tanks and pickup and kicker electrodes are listed intable 3.7.1. As the frequency of the system increases, the size of the electrodes and theirspacing along the beam shrink. Therefore, the higher frequency systems have a higherlongitudinal density of electrodes.

Table 3.7.1: Number of pickup and kicker tanks and electrodes required tofulfill the cooling requirements outlined in chapter 2.

Plane Band(GHz)

PickupTanks

KickerTanks

PickupElectrodes

KickerElectrodes

Horz 2-4 1 1 32 32Vert 2-4 1 1 32 32Mom 1-2 2 2 32 32Mom 0.5-1 2 2 16 16

Total 6 6

The standard length of a tank is 48". A typical array is 1 m long. Therefore, onlythree tanks per half cell fit into an unmodified section of Recycler lattice.

3.7.3. Laser Telescope

The laser telescope is composed of two passive elements per beam, each pair oneither side of the telescope. First, in order to minimize the laser beam divergence thebeam radius is increased via large aperture telescope lens systems at either end of theevacuated tubes. With a 20:1 expansion ratio, the laser beam can be as large as 2" indiameter. Second, the transitions of the laser light from fiber optic cable to air and backare accomplished with a light launcher composed of a polished fiber end coupled to apoint-to-parallel collimating lens.

As shown in figure 3.7.3, there are also X-Y micro-positioning stages to move thelight launcher transversely with respect to the beam expander and to steer the entire beamin either dimension. These stages are operated via remote control and/or feedback loopsto set and maintain a high quality optical link across the arc of the Recycler.


FiberOpticCable

LightLauncher

Beam Expander

X-Y PositionStage

X-Y AngleManipulator

2"

Figure 3.7.3: Sketch of the optics involved in the laser telescope. Thepassive optical hardware is identical on both sides of the telescope.

3.8. Instrumentation (WBS 3.1.8)

The Recycler Ring instrumentation will closely resemble much of the Main Injectorinstrumentation. The beamline intensity monitors and both the longitudinal andtransverse wideband detectors will be identical. Some changes will occur in thetransverse Schottky system to take advantage of the stationary revolution frequency of theRecycler. A commercial beam current measurement system will be purchased. Due tocosts and unusual beam signals, the beam position monitor system is very unique.

3.8.1. Beam Position Monitor System

The BPM (Beam Position Monitor) detectors will be used for both positioninformation and ion clearing. In the Recycler ring 416 detectors located at the 1/3 and2/3 boundaries of each half cell will provide 8 detectors per betatron wavelength in boththe horizontal and vertical planes. Split-plate detectors will provide output linear withdisplacement in one plane at a time. Three flavors of detector will be required: onehorizontal and one vertical elliptical detector, covering most of the ring; and one rounddetector, rotated to measure the desired plane. Detector edges will be rounded to preventarcing of the ion-clearing high voltage.

The BPM system will have two measurement modes. The first measures injectedbeam from the Booster or Main Injector, while the second measures the closed orbit ofthe stack. The beam stack in the Recycler will be DC beam, except for an injection gapequal to 1/7th of the circumference. For both modes, the resulting harmonics of the 89.8kHz revolution frequency lead to an AC-coupled pulse for low frequency processing.

The low and medium frequency response of the detector resembles that of a highpassfilter. The low frequency corner is inversely proportional to both the terminatingresistance and the system capacitance. For long cable runs terminated in high impedance,sensitivity is inversely proportional to the cable capacitance. These two factors dictatethe use of high-impedance pre-amplifier buffers in the tunnel. A series resistance beforethe pre-amp reduces the system bandwidth and noise. The radiation resistance of possiblepre-amp candidates is being tested in the Booster dump. Manufacturer testing [AnalogDevices, Inc., Radtest Data Service, November 1995] claims radiation resistances of 25-


50 and 200 kRad for two possible chips. Other possibilities, including discretetransistors, are being considered.

Tunnel Serv. Bldg.

Mode

BeamSync

toMADC

RG58 120’-1300’

S&HLogamps

Log B

A

B

chokes

pre-amp

HV Timingmodule

Log A

–15v

Cal

Figure 3.8.1: Block Diagram of the Recycler BPM System.

Short cables will connect detector feedthroughs to a small shielding box for the pre-amps and other components. The box, shared by two neighboring detectors, may bemounted above the Recycler magnets for enhanced radiation shielding. A high resistancecouples the high DC voltages to the detector plates for ion clearing. The high voltagesare daisy-chained for all the detectors in a sector. Current monitoring takes place at thesource of these voltages, in the service buildings. A calibration signal, resembling atypical signal pulse, will also be daisy-chained throughout a sector. When activated, itwill be loosely coupled equally to the two signal paths.

The low signal frequencies enable use of inexpensive RG58 50Ω cable for the 120'-1300' cable runs. Additional cables are needed for the two pre-amp DC supplies, the ion-clearing high voltage, and the calibration signal. Dual use of cables for DC and ACsignals is being considered. Figure 3.8.1 contains a sketch of the BPM system.

The cost constraints of the Recycler project and the nature of the detector signalsdemand a new, inexpensive processing scheme and control system interface. Innovationsin analog processing technology and the Fermilab control system make that possible.

The position can be derived from the signals of a linear detector by

x[mm]b[mm]

= A − BA + B

≈ Ln10

2logA − logB( ) , (3.8.1)

where A and B are amplitudes of the two plate signals and b is the detector radius.Recent improvements in logarithmic amplifiers [Analog Devices, Inc., AD640 andAD608 data sheets, Analog Devices Design-In Reference Manual, 1994] enable a largedynamic range and high bandwidth. Laboratory tests on a simulated Recycler signalshow a dynamic range near 50 dB. These chips approximate the log function. Lognonconformance, which leads to errors, is expected to fall within the accuracyspecification. Subtraction by a differential op-amp results in a voltage which is converted


to position after system (detector and electronics) offset subtraction and scaling. This canbe carried out in the control system.

The position signal will be digitized using standard MADC-compatible ADCs fromthe Controls Department. The result is interfaced to the control system with the CAMAC290 MADCs. The differing signal occurrence times at the BPMs (a range of 2 µs persector for both protons and antiprotons) and the two operating modes (injection andstack) require a sample-and-hold circuit with correct timing. From the 1.6 µs minimumsignal length, acquisition time, and other factors, it is anticipated that 6 distinct timingsignals are needed per house. These will be created with CAMAC 279 modules,synchronized to the Recycler Ring Beam Sync clock.

The digitized signals are converted into ACNET database devices with scaling asdescribed above. Standard acquisition types will be available, including "snapshot"(closed-orbit), "flash" (single-turn), and turn-by-turn (TBT). Note that only one TBTchannel is possible per MADC, and current plans call for two MADCs per house. Anapplication page will control acquisition modes and timings, as well as calibrations doneduring beam-off times.

3.8.2. Beam Loss Monitor System

The Recycler Ring will use the beam loss monitor system of its neighbor, the MainInjector. There will be no additional monitoring for the Recycler.

3.8.3. Longitudinal Wideband Pickup

One resistive wall current longitudinal pickup will be built for the Recycler andplaced in the MI-30 region. The design will be identical to that used for the MainInjector. It will be used for studies and any possible longitudinal monitoring systems.

The basic design of this resistive wall current monitor is to insert a ceramic gapshunted with resistance in the vacuum pipe and measure the voltage induced by the beamwall current [R. Webber, "Longitudinal Emittance an Introduction to the Concept andSurvey of Measurement Techniques Including Designing of a Wall Current Monitor",AIP Acc. Instr. Conf. Proc. #212, 1989]. The ultimate bandwidth of such a detector islimited by the spreading of the electric field lines between the beam and the image chargeon the inside wall. For the monitor's 5" circular aperture and the relativistic Recyclerbeam, the bandwidth limit is 23 GHz.

In practice the detector response is difficult to maintain above the microwave cutofffrequency of the beam pipe, estimated to be 1.4 GHz for the 5" diameter. Spuriouselectromagnetic energy, generated by various discontinuities and guided along the beampipe, corrupts the image current signal. Microwave absorber material is placed inside a6" vacuum pipe up and downstream of the detector to reduce this noise by 20 dB. Theabsorbing material is an epoxy-based Resin Systems RS4825 core. It is placed outside a5" aperture ceramic sleeve to preserve vacuum specifications without lessening theabsorbing properties. This solution is cheaper and more readily available than theprevious vacuum-friendly absorber.

The detector maintains a 3 kHz low frequency cutoff with a series of toroids shuntingthe resistance across the gap. An impedance of 1Ω (122 resistors of 112Ω each)terminates a radial transmission line formed by the 140 mil ceramic gap. Four signal


pickoff points spaced evenly around the gap are summed to reduce position dependenceand azimuthal signals. The result is a position-independent longitudinal monitor with ±1dB flat response from 3 kHz to 6 GHz, as measured with a tapered 50Ω transmission linetest setup. An identical, reciprocal port can be used for calibration.

3.8.4. Transverse Wideband Pickups

The Main Injector transverse wideband pickup design will be used in the Recycler.Two pickups, one for each plane, will be placed at MI-30 for studies purposes.

Standard striplines are planned for both the horizontal and vertical planes.Feedthroughs at both ends will be used to observe both proton and antiproton signals.The plate length of 55", λ /4 at 53 MHz, will be used to increase signal and to maximizedoublet separation when viewing proton injections. In the frequency domain, zeroes intransmission will occur at those frequencies where the plate is λ/2 long.

3.8.5. Transverse Profile Monitors

The Ionization Profile Monitor (IPM) system [Zagel, J., "Fermilab Booster Ion ProfileMonitor System Using LabView", AIP Acc. Instr. Conf. Proc. #333, 1994], used in theBooster and Main Ring/Main Injector, is planned for the Recycler Ring. Two systemsare needed to handle the transverse planes. The IPM uses a microchannel plate to collectand amplify ions produced when the beam passes through residual gas in the detector.The high quality vacuum in the Recycler may necessitate an intentional, localized,calibrated gas leak at the IPM detector.

The 8 kV clearing field of the Booster IPM sweeps the ions across the 10 cm apertureonto a microchannel plate, which amplifies the current and deposits it onto a grid of 1.5mm spaced conductors etched into a printed circuit card. The current induced in eachconductor is amplified, digitized, and stored each turn. The amplifiers have a gain of 2.5X 106 volts per amp and 100 kHz bandwidth. The digitizers are commercial 4 channel12 bit VME cards which have 64 Kwords of memory for each channel. A NationalInstruments MXI adapter is used to access the VME cards with a Macintosh computerrunning LabView software. The Main Ring IPMs use a 20 kV clearing field across the10 cm aperture with 0.5 mm conductor spacing on the collection grid.

A flying wire system is not being included due to the high reliability demanded of theRecycler ring. The possibility of the failure mode of the wire getting stuck in beam wasconsidered too great.

3.8.6. Transverse Schottky Monitor

The Recycler Ring transverse Schottky monitor system [Chou, P., "TransverseSchottky Detector for Antiproton Recycle Ring", internal Fermilab note] will be similarto the new Main Ring system but with much higher sensitivity. The primary systemoutput is a two channel (for two planes) spectrum analyzer display in the main controlroom. Various beam parameters can be calculated from information provided bytransverse Schottky signals, including fractional tune, transverse emittance, momentumspread, chromaticity, and presence of trapped ions [Peterson, D., "Schottky SignalMonitoring at Fermilab", AIP Acc. Instr. Conf. Proc. #229, 1990].


The two Schottky detectors, to be located at MI-30, will be round, split-platecapacitive pickups. A box in the tunnel will contain a transformer, designed to resonatethe detector at 79.263 MHz and to couple to the output cable. The resonant frequencywas chosen at the harmonic number n=882.5, halfway between the first two harmonics ofthe Main Injector RF system. A bandwidth of 90 kHz (one revolution harmonic) requiresa loaded quality factor QL=880. To enable this high Q and maintain stability, suitablefeedthroughs must be found and temperature drift effects must be small. The detectorsensitivity is given by

S⊥ = l2 bc

Ro ωc QoCt

, (3.8.2)

where l is length, nominally 40 cm, b is aperture radius, c is speed of light, Ro is thereceiver's 50Ω termination, ωc is radian resonant frequency, Qo is unloaded Q, and Ct istotal capacitance. Design calculations estimate a sensitivity of 22 Ω/mm, much higherthan the Main Ring system (0.9 Ω/mm) and comparable to the Tevatron's (27 Ω/mm).Low-loss heliax 50Ω cables will be used to bring the signals upstairs.

50 Ω heliax cable output

Figure 3.8.2: Sketch of the Recycler transverse Schottky electrical model.The split plate pickup provides a linear position response function. Thesystem is resonated at 79.263 MHz (n=882.5).

The Schottky receiver down-converts the signal bandwidth to baseband for use with alow frequency spectrum analyzer. A Trontech ultra-low noise amplifier provides 60 dBof gain. Variable attenuators tune the gain. Custom crystal bandpass filters from PiezoTechnology, Inc. set the signal bandwidth at 100 kHz. The local oscillator signal mightbe generated by a Main Injector injection frequency oscillator, if available, or a fixedcustom oscillator. Unlike the Main Ring/Main Injector, the Recycler energy is constantat 8.9 GeV. Thus, its revolution harmonics will remain fixed and no frequency trackingis needed. A mixer down-converts the signal before a final low-pass filter and gain stage.A long length of RG-8 low loss cable brings the outputs to the Main Control Room andthe spectrum analyzer. Given that a horizontal and vertical system are needed, thisimplies 2 cables to the control room and two channels of FFT capable digitizers.


60 dB

79.263 MHz3 dB BW= 100 kHz

50 Ω heliax cable

R

Σ÷2

frequencydividerMain Injector

rf sync, h= 588

79.263 MHz3 dB BW= 100 kHz

L

79.218 MHzn= 882

I

3 dB BW= 100 kHz,20 dB gain

20 dBrange

output

resonate atn= 882.5

Figure 3.8.3: Sketch of the beam processing electronics which conditionsthe RF signal from the detector to a low frequency signal a signal analyzercan measure.

3.8.7. Ring Current Monitor (DCCT)

The DC Current Transformer, or parametric current transformer, uses the secondharmonic detection principle to measure the DC beam current in series with an ACtransformer to extend the bandwidth (Unser, K., "The Parametric Current Transformer, abeam current monitor developed for LEP", AIP Acc. Instr. Conf. Proc. #252, 1991).Fermilab does have a number of versions of the DCCT, but a commercial version will bepurchased for a Recycler unit at MI-30. The Bergoz current monitor (Bergoz, ParametricCurrent Transformer data sheet) is 4.25" long and offers several apertures from 2" to 7".At this time, a 3" pipe is anticipated at MI-30. A ceramic break is required for use withthe Bergoz monitor. Radiation damage can be reduced by selecting the radiation hardsensor option and locating the tunnel front-end electronics (maximally 5 m from thesensor) where radiation dosage is less than 104 rad/year.

The DC current monitor is relied upon for absolute beam current calibrations. TheBergoz monitor specifies a frequency response from DC-20 (optionally 100) kHz,dynamic range of 2 X 107 for each full scale range, resolution optionally to 0.5 µA, andabsolute accuracy and linearity of 0.05% and 0.01%, respectively. The ±10V output isdigitized and interfaced to the controls system with the MADC.

3.8.9. Toroids

Toroid systems are AC-coupled intensity monitors that are cheaper than DCCTs andappropriate during transient events such as injections and extractions. The present toroiddesign used Pearson Electronics, Inc. model number 3100 current monitors. The apertureis 3.5" and the output signal is 0.5 volts/amp into 50Ω with a bandwidth of 40 Hz to7 MHz. At the toroid output the signal is 85 mV for 1010 ppb. The toroid is electricallyisolated from ground in the enclosure and good quality cable such as LDF4-50A is


required to avoid noise problems. The toroid must be placed over a ceramic break in thevacuum pipe. To reduce the RF energy radiated into the environment a groundconnection is required across the break but external to the toroid.

The signal is transported to the service building where the electronics amplifies, limitsthe bandwidth, and integrates the signal to provide a voltage representing the total charge.The present design [Vogel, G., "Toroid Integrator User Guide", internal Fermilab note] inuse includes a baseline subtraction circuit, a fixed length integration window, and an A/Dand D/A used to form a sample and infinite hold. The toroid integrator has a bandwidthof 100 Hz to 400 kHz and selectable gains of 2x1011, 2x1010, and 2x109 particles/volt.

There are 6 toroid systems required due to the addition of the Recycler Ring.Figure 3.8.4 shows the relative locations of these systems. For each transfer between theMain Injector and the Recycler there are 3 toroids; one to determine the initial intensity,one record the transfer line intensity, and finally one to measure the final intensity. Forthe abort line there is an initial intensity and an abort line intensity.

L LK

L L LK K

MI

RR

MI-30MI-40 MI-20

Figure 3.8.4: Sketch of the placement and number of toroids in the MainInjector and Recycler to service the instrumentation needs of the Recyclertransfers. The Lambertsons (L), kickers (K), and toroids (black dots) areshown with respect to the service building the reside in.

3.9. Controls (WBS 3.1.9)

Controls requirements have been the focus of a number of cross-departmentaldiscussions. Because of the novel nature of many of the technologies employed in theRecycler ring, it is important that a thorough exploration of hidden demands on controlsbe identified. Just as in the case of beam instrumentation, it is vital for efficientcommissioning of the Recycler that all control software and hardware be installed andtested before actual accelerator commissioning commences. Below is the result of thesescope explorations.

3.9.1. Stochastic Cooling System

Existing equipment will be moved from the present Tevatron bunched beamstochastic cooling R&D implementation. CAMAC equipment now residing at F0 TeVcrates $60, $61, $62 will be moved to their new locations at MI-20 and MI-30.


3.9.2. Power Supplies

The two kickers in the Recycler and one kicker in the Main Injector will need powersupply controllers - CAMAC C118 cards and beam synch triggers supplied by C279cards. All associated Lambertsons are built with permanent magnets and do not requirepower supply controls.

There are a number of dipole correctors required in the Recycler ring and its transferlines. Around each of the 3 Recycler Lambertsons a 4-bump orbit offset is required inboth planes. This requirement alone involves 24 correctors. In the transfer and abortlines another 20 correctors are required. Figure 3.3.1 contains a sketch of the correctorcount and placement.

In addition to the dipole correctors, the phase trombone quadrupoles, the two skewquadrupoles at MI-60, and the correction sextupoles at MI-20 and MI-50 are alsopowered with Main Ring ramped corrector chasis.

All correctors will utilize existing MR corrector power supplies and existing correctorcoils, each chassis controls 6 correction elements. A total of 8 of these supplies arerequired: 2 at MI-20, 4 at MI-30, and 2 at MI-40. It should be noted that additional bulkpower supply control in addition to what CAMAC 053 cards can provide is required. SixCAMAC 118 cards will be included to cover this need.

3.9.3. RF Systems

The low level RF system developed for the Recycler RF system, which is a copy ofthe VXI MI LLRF system, will be located at MI-60. It will need an accelerator controlsethernet connection to the VXI platform.

3.9.4. GPIB Interfaces

Stochastic cooling, RF, and instrumentation all need GPIB connections. There willbe an interface at MI-20, MI-30, and MI-60 (assuming up to 32 devices per connection).A high speed and reliable VME based interface will be used.

3.9.5. Vacuum System

There will be one ion pump for every 2 half cells (104 total) for the Recycler itself.There will also be 4 pumps for each of the transfer lines (16 total). Each pump requirescontrol and monitoring. No automatic valves (other than the safety critical devices) willbe allowed in the Recycler in order to eliminate the chance of accidental antiproton stackloss. All of the valves will be manually operated. The positions of these manual valveswill not be electronically monitored. Instead, valve motion will only be allowed via theinsertion of keys which can only be removed when the valves are in the out position. Thekeys are put in a low-tech key tree to make up a permit. The requirement for gauges istwo ion gauges per vacuum sector (every 8 cells for a total of 13 sectors and 26 gauges).CIA crates are the best way to effect control of Recycler pumps. Spare control channelsare available in planned Main Injector CIA crates at 4 of the 6 service buildings. TwoCIA crates (and ARCNET controllers) will be purchased for the other service buildings.One CIA card can control 6 pumps. Some spare gauge channels will be used by theRecycler. Sharing CIA crate space with the Main Injector vacuum system will not


present any software problems. Summary of ring and transfer line (XL) pumps and theirgeographical position are summarized in table 3.9.1.

Table 3.9.1: Summary of the Recycler pump controller locations aroundthe ring. Transfer line (XL) pumps are also included in the count.

Service Bldg # of Cells Ring Pumps XL Pumps Total Pumps

MI-10 16 16 0 16MI-20 16 16 0 16MI-30 20 20 8 28MI-40 16 16 2 18MI-50 16 16 0 16MI-60 20 20 0 20Totals 104 104 10 114

3.9.6. Beam Position Monitors (BPM)

It is possible to support the Recycler BPM system with existing multiplexed ADC(MADC) and CAMAC 290 card controllers dedicated to this function. Scans of theclosed orbit can occur every 1 to 2 seconds. Turn-by-turn beam position acquisition isalso supported. For turn-by-turn data taking, the MADCs (and controllers) must be fastenough to accommodate the Recycler's 90 kHz revolution frequency. A minimum 12 bitresolution for the MADC has been specified.

There is one horizontal and one vertical BPM every half cell, for a total of 416Recycler ring beam position measurements. Intensity signals will not be provided by theBPM RF modules. Horizontal and vertical monitors are distributed to separate MADCsto facilitate acquiring turn-by-turn data. This will require at least two MADC systems perhouse (service building). Connection to the sample and hold analog outputs of the BPMsshould be direct and use 16 twisted pair cable for direct connection to the MADC.Avoiding use of an Analog Entry Box will save costs.

Table 3.9.2: Summary of BPM MADC system counts and locations.

Service Bldg # Cells Horz BPMs Vert BPMs XL BPMs Total BPMs

MI-10 16 32 32 0 64MI-20 16 32 32 0 64MI-30 20 40 40 28 108MI-40 16 32 32 8 72MI-50 16 32 32 0 64MI-60 20 40 40 0 80Totals 104 208 208 36 452

Associated control of BPM data acquisition requires generation of a "sample" signaltriggered by a RRBS event. Also required at each service building are four CAMAC


279 cards listening for the sample event to provide appropriately timed triggers to theBPM module's sample-and-hold (S&H) circuit. The data taking mode of the CAMAC290 cards is controlled by TCLK events and software. A timing resolution of 1 µsec isrequired for BPM signal sampling.

There are also BPMs associated with each of the transfer lines. These are included intable 3.9.2 as "XL BPM", with half being horizontal and the other half vertical. The ringbeam sync timing will also serve to trigger the S&H circuits of the transfer line BPMs.

3.9.7. Control System Front Ends

Recycler controls requirements do not require an additional front end computer.Specialized instrumentation systems such as residual gas ionization profile monitorsusing Macintosh computers running the LabView software are connected directly to theethernet link around the ring.

3.9.8. Accelerator Control Consoles

An MI-30 control room for Recycler commissioning and electron cooling research,development, and eventual commissioning will need two consoles.

3.9.9. Beam Permit System:

Because of the precious nature of antiprotons, the beam permit system will only beapplied to protons during commissioning. The Recycler beam permit system status willbe applied to the beam switch sum box (BSSB) to adjudicate injection of protons.CAMAC 200 cards, input panels, and repeaters will be installed at each of the 6 MainInjector service buildings and the main control room. All equipment should be availablefrom the MR system after decommissioning. The beam permit will be physicallyimplemented with a spare optical fiber.

3.9.10. Recycler Ring Beam Sync Clock (RRBS)

The low level RF system will provide: a revolution marker (53 MHz/588); 7.5 MHz(53 MHz/7), and 53 MHz. Various CAMAC modules are necessary for clock generationand have been added to the WBS. These will be located at MI-60 and include twoCAMAC 377 cards, a CAMAC 280, 175, and 276 card. These signals will be supportedring-wide and at the main control room, so at least 12 fiber repeaters are necessary.RRBS will use a spare optical fiber.

3.9.11. Software

Unlike the Main Injector, in which most systems existed previously in the Main Ring,the Recycler relies on new subsystems, new geometries, and hence new software.Because of the traditional tendency to underestimate software manpower requirements,serious discussions of the scope of software requirements have been held. Below are theresults of these discussions.

Database entries: The stochastic cooling system gets transferred from the Tevatron.Everything else is created new. Because of the use of permanent magnets, the non-


existence of distributed corrector systems, and the lack of utilities, the total number ofdatabase entries is <1000. A new "R" index page will be created and R:xxxxxx databaseentries will be facilitated.

Applications: After studying the applications driving the other Fermilab accelerators,a list of programs relevant to the Recycler ring has been developed. Some of theapplications are rather generic, such as DataLogger, vacuum readback, and parameterpages. The orbit control/magnet move program is very important, and is already appliedto Fermilab accelerators. With the addition of the Recycler lattice to the programdatabase, it will be able to function with minimal modification. Similarly, the stochasticcooling software already exists from the Tevatron Collider bunched beam cooling effort.New programs for low level RF control and beam position measurement must be written.Just as the number of database entries is orders of magnitude smaller than otheraccelerators, the number of application programs is similarly low.

3.10. Safety System (WBS 3.1.10)

The additional safety system components necessary to support the Recycler are quitelimited. To insure the termination of the coasting beam in the Recycler, two gravityactivated fail safe vacuum isolation gate valves will be used. These valves are necessarybecause permanent magnets cannot be readily turned off and interlocked.

3.11. Utilities (WBS 3.1.11)

Besides a limited amount of conventional power, the only utility being used by theRecycler is LCW. The subsystems which consume this water are described below. Allusages are in service buildings. Note that the total water flow required by the Recycler isapproximately 40 gallons/minute. There are sometimes leaks in the Main Ring that arelarger than this!

3.11.1. Dipole Corrector Supplies

The dipole correctors supplies at MI-10, MI-30, and MI-40 require 4 gallons/minuteper chassis. Each chassis services 6 correctors. Table 3.11.1 summarizes this usage.

Table 3.11.1: Summary of LCW water usage rates at each service buildingin which a need exists for the ring and its dedicated transfer lines.

Location # Chassis LCW Need

MI-20 4 6 gal/minMI-30 4 16 gal/minMI-40 2 8 gal/minMI-50 2 8 gal/minMI-60 2 8 gal/min


3.11.2. Stochastic Cooling Traveling Wave Tubes

The stochastic cooling kickers at MI-30 are driven by traveling wave tubes (TWT)which require a couple of gallons per minute per tube. Given that there are three coolingchannels, a total of approximately 6 gal/minute is required.

3.11.3. Moving Existing LCW Pipes

There are a limited amount of valves, pipes, and air dehumidifiers which have alreadybeen installed in the MI-60 straight section which will have to be moved because of theaddition of the Recycler. In addition, in order to build the MI-22 and MI-32 transfer linesbetween the Main Injector and Recycler the LCW headers in the regions between Q212 &Q222 and Q320 & Q330 need to be moved.


4. Civil Construction

In this section the civil construction associated with the Recycler project is described.The purpose of this work is to construct both the penetrations for the stochastic coolingfiber optic cables and the laser telescopes for signal transmission between the pickup andkicker tanks.

4.1. Stochastic Cooling Penetrations

The penetrations for the stochastic cooling system are situated at Main Injectorquadrupole locations Q213 and Q109. As shown in figure 4.1.1, a 2" diameter pipebetween the berm toe line and the tunnel is inserted in order to provide a conduit foralignment control cables and fiber optic signal transmission lines. This pipe is placed in ahole bored by a drilling crew.

~30 ft.

Recycler

Main Injector

berm

Figure 4.1.1: Tunnel and berm cross-section with a 2" diameter conduit forstochastic cooling signal transmission via optical fibers. In addition, thealignment control cables for aiming the laser beams and the electricalservice for the required pumps and motion control must also fit in theconduit.

4.2. Stochastic Cooling Telescope

Approximately 8' below the surface near Q213 the horizontal, vertical, and twomomentum stochastic cooling signals, transmitted as AM modulation on four separatelaser beams, are aimed toward the Q109 location. The transition from optical fiber to a1" diameter laser beam (and back to fiber optic again) is accomplished with commercialoptical components. All of these components are passive and do not require power. The


lasers are aimed through a window into an evacuated pipe for signal transmission. Thepipe has a diameter of 18" and is 3/16" thickness stainless steel coated for cathodiccorrosion protection.

In order to aim the laser beams, it is necessary to have remote piezoelectric motioncontrol. The power, control, and diagnostic readback cables for aiming come from thetunnel. The exact location of this optical transition/aiming hardware is at presentdesigned to be approximately 8' underground. In order to assure maximum stabilityagainst transverse pipe motion, the pipe is buried below the frost line. Because theaiming mechanism is below ground, and that hardware must be installed and maintained,a manhole accessed underground enclosure is required on both sides of the telescope.These enclosures require sump pumps in order to keep the aiming hardware and opticalfibers dry. The power for the sump pumps also comes from the tunnel via the stochasticcooling penetrations discussed in section 4.1. A sketch of an enclosure appears infigure 4.2.1.

5'

Ground Level

Sump Discharge

Manhole

AccessLadder

8'

EvacuatedTelescopeTubes

Stochastic CoolingPenetration

Telescope& AimingHardware

16'

16'

4'

RoughingVacuum Pump

Figure 4.2.1: Sketch of one of the enclosures required at each end of thestochastic cooling signal telescope. One inexpensive model for thisenclosure is a sewer access manhole constructed of round, pre-fabricatedconcrete components.

Therefore, the civil construction implications of the stochastic cooling telescope are;1) the excavation of an 8 ft. deep and 1800 ft. long trench for burial of the signaltransmission pipes, and 2) the construction of two human accessible undergroundenclosures on either side of the telescope.

fermilab recycler ring technical design report · ring to provide more detailed and precise...

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